Integer sequences related to Boolean functions

Studies of Boolean functions

## number of equivalence classes

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See also .../clans.

name  | equivalent under  | maximum size  | sequence  | 0 | 1 | 2 | 3 | 4 | 5

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family | neg  |  2 n {\displaystyle 2^{n}} | A000231 | 2 | 3 | 7 | 46 | 4336 | 134281216
splinter  | intersection of family and faction | TBA7 | 2 | 4 | 14 | 184 | 51564 |
faction | perm  |  n ! {\displaystyle n!} | A003180 = 2 · A000612 | 2 | 4 | 12 | 80 | 3984 | 37333248
great faction  | complementary and partner factions | A003180(n) / 4 for n > 0 | 1 | 1 | 3 | 20 | 996 | 9333312
clan | neg, perm  |  2 n ⋅ n ! {\displaystyle 2^{n}\cdot n!} | A000616 | 2 | 3 | 6 | 22 | 402 | 1228158
super-family
blunt family  | neg, comp  |  2 n + 1 {\displaystyle 2^{n+1}} | A000133 | 1 | 2 | 5 | 30 | 2288 | 67172352
super-clan
blunt clan  | neg, perm, comp  |  2 n + 1 ⋅ n ! {\displaystyle 2^{n+1}\cdot n!} | A000370 | 1 | 2 | 4 | 14 | 222 | 616126

## by weight

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A054724 number of families by weight
A039754 number of clans by weight

### balanced

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| 1 | 2 | 3 | 4 | 5

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families  | balanced  | TBA1 (central values of A054724) | 1 | 3 | 14 | 870 | 18796230
self-complementary  | A001320 | 1 | 3 | 14 | 240 | 63488
clans  | balanced  | A000721 (central values of A039754) | 1 | 2 | 6 | 74 | 169112
self-complementary  | A000610 | 1 | 2 | 6 | 42 | 4094

## representatives of equivalence classes

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A227722 (families) and A227723 (clans) show smallest values corresponding to truth tables. Which Boolean function an integer represents, depends on the arity.

In the following the representative is always the smallest Zhegalkin index.

families   TBA4

The length of the sequence for arity n is A000231(n), the number of n-ary families.

| n |  | sequence

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0  | 2  | 0, 1,
1  | 1  | 2,
2  | 4  | 4, 6, 8, 9,
3  | 39  | 16, 18, 20, 22, 24, 32, 33, 36, 40, 41, 44, 64, 65, 66, 72, 73, 74, 96, 97, 98, 104, 106, 107, 128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151,
4  | 4290  | 256, 258, 260, 262, 264, 272, 274, 276, 278, 280, 288, 292, 296, 300, 320, 322, 328, 330, 352, 354, 360, 362, 384, 386, 388, 390, 400, 402, 404, 406, 512, 513, 516, 520, 521, 524, 528, 532, 536, 540, 544, 545, 548, 552, 553, 556, 560, 564, 568, 572, 576, 577, 584, 585, 608, 609, 616, 617, 640, 641, 644, 645, 656, 657, 660, 661, 704, 705, 708, 709, 720, 721, 724, 725, 1024, 1025, 1026, 1032, 1033, 1034, 1040, 1042, 1048, 1050, 1056, 1057, 1064, 1065, 1088, 1089, 1090, 1096, 1097, 1098, 1104, 1106, 1112, 1114, 1120, 1121, 1128, 1129, 1152, 1153, 1154, 1155, 1168, 1169, 1170, 1171, 1184, 1185, 1186, 1187, 1200, 1201, 1202, 1203, 1536, 1537, 1538, 1544, 1546, 1547, 1552, 1554, 1560, 1562, 1568, 1569, 1576, 1577, 1600, 1601, 1608, 1609, 1632, 1633, 1634, 1640, 1642, 1643, 1648, 1650, 1656, 1658, 1664, 1665, 1666, 1667, 1680, 1681, 1682, 1683, 1696, 1697, 1698, 1699, 1712, 1713, 1714, 1715, 2048, 2049, 2050, 2051, 2052, 2053, 2054, 2055, 2064, 2066, 2068, 2070, 2080, 2081, 2084, 2085, 2096, 2097, 2100, 2101, 2112, 2113, 2114, 2115, 2128, 2129, 2130, 2131, 2144, 2145, 2146, 2147, 2160, 2161, 2162, 2163, 2176, 2177, 2178, 2179, 2180, 2181, 2182, 2183, 2192, 2194, 2196, 2198, 2208, 2209, 2212, 2213, 2224, 2225, 2228, 2229, 2240, 2241, 2242, 2243, 2256, 2257, 2258, 2259, 2272, 2273, 2274, 2275, 2288, 2289, 2290, 2291, 2304, 2305, 2306, 2307, 2308, 2309, 2310, 2311, 2320, 2322, 2324, 2326, 2336, 2337, 2340, 2341, 2352, 2353, 2356, 2357, 2368, 2369, 2370, 2371, 2384, 2385, 2386, 2387, 2400, 2401, 2402, 2403, 2416, 2417, 2418, 2419, 2432, 2434, 2436, 2438, 2448, 2449, 2450, 2451, 2452, 2453, 2454, 2455, 2464, 2465, 2468, 2469, 2480, 2481, 2484, 2485, 2496, 2497, 2498, 2499, 2512, 2513, 2514, 2515, 2528, 2529, 2530, 2531, 2544, 2545, 2546, 2547, 4096, 4097, 4098, 4100, 4102, 4104, 4105, 4128, 4129, 4130, 4132, 4134, 4136, 4137, 4160, 4161, 4162, 4164, 4166, 4168, 4169, 4192, 4193, 4194, 4196, 4198, 4200, 4201, 4224, 4225, 4226, 4227, 4228, 4229, 4230, 4231, 4232, 4233, 4234, 4235, 4236, 4237, 4238, 4239, 4608, 4609, 4610, 4612, 4614, 4616, 4617, 4640, 4642, 4643, 4644, 4646, 4648, 4649, 4672, 4673, 4680, 4681, 4682, 4684, 4686, 4704, 4705, 4712, 4714, 4715, 4716, 4718, 4736, 4737, 4738, 4739, 4740, 4741, 4742, 4743, 4744, 4745, 4746, 4747, 4748, 4749, 4750, 4751, 5120, 5121, 5122, 5124, 5126, 5128, 5129, 5152, 5153, 5160, 5161, 5162, 5164, 5166, 5184, 5186, 5188, 5189, 5190, 5192, 5193, 5216, 5217, 5224, 5226, 5228, 5229, 5230, 5248, 5249, 5250, 5251, 5252, 5253, 5254, 5255, 5256, 5257, 5258, 5259, 5260, 5261, 5262, 5263, 5632, 5633, 5634, 5636, 5638, 5640, 5641, 5664, 5665, 5672, 5674, 5675, 5676, 5678, 5696, 5697, 5704, 5706, 5708, 5709, 5710, 5728, 5730, 5732, 5734, 5735, 5736, 5737, 5760, 5761, 5762, 5763, 5764, 5765, 5766, 5767, 5768, 5769, 5770, 5771, 5772, 5773, 5774, 5775, 6144, 6145, 6146, 6147, 6148, 6149, 6150, 6151, 6152, 6153, 6154, 6155, 6156, 6157, 6158, 6159, 6176, 6177, 6178, 6179, 6180, 6181, 6182, 6183, 6184, 6185, 6186, 6187, 6188, 6189, 6190, 6191, 6208, 6209, 6210, 6211, 6212, 6213, 6214, 6215, 6216, 6217, 6218, 6219, 6220, 6221, 6222, 6223, 6240, 6241, 6242, 6243, 6244, 6245, 6246, 6247, 6248, 6249, 6250, 6251, 6252, 6253, 6254, 6255, 6272, 6273, 6274, 6275, 6276, 6277, 6278, 6279, 6280, 6281, 6282, 6283, 6284, 6285, 6286, 6287, 6304, 6305, 6306, 6307, 6308, 6309, 6310, 6311, 6312, 6313, 6314, 6315, 6316, 6317, 6318, 6319, 6336, 6337, 6338, 6339, 6340, 6341, 6342, 6343, 6344, 6345, 6346, 6347, 6348, 6349, 6350, 6351, 6368, 6369, 6370, 6371, 6372, 6373, 6374, 6375, 6376, 6377, 6378, 6379, 6380, 6381, 6382, 6383, 8192, 8193, 8194, 8195, 8196, 8198, 8200, 8201, 8204, 8205, 8208, 8209, 8210, 8211, 8212, 8214, 8216, 8217, 8220, 8221, 8256, 8257, 8258, 8259, 8260, 8261, 8262, 8263, 8264, 8265, 8266, 8267, 8268, 8269, 8270, 8271, 8320, 8321, 8322, 8323, 8324, 8326, 8328, 8329, 8332, 8333, 8336, 8337, 8338, 8339, 8340, 8342, 8344, 8345, 8348, 8349, 8384, 8385, 8386, 8387, 8388, 8389, 8390, 8391, 8392, 8393, 8394, 8395, 8396, 8397, 8398, 8399, 8448, 8449, 8450, 8451, 8452, 8454, 8456, 8457, 8460, 8461, 8464, 8465, 8466, 8467, 8468, 8470, 8472, 8473, 8476, 8477, 8512, 8513, 8514, 8515, 8516, 8517, 8518, 8519, 8520, 8521, 8522, 8523, 8524, 8525, 8526, 8527, 8576, 8578, 8580, 8581, 8582, 8583, 8584, 8585, 8588, 8589, 8592, 8594, 8596, 8597, 8598, 8599, 8600, 8601, 8604, 8605, 8640, 8641, 8642, 8643, 8644, 8645, 8646, 8647, 8648, 8649, 8650, 8651, 8652, 8653, 8654, 8655, 9216, 9217, 9218, 9219, 9220, 9221, 9222, 9223, 9224, 9225, 9226, 9227, 9228, 9229, 9230, 9231, 9232, 9233, 9234, 9235, 9236, 9237, 9238, 9239, 9240, 9241, 9242, 9243, 9244, 9245, 9246, 9247, 9280, 9281, 9282, 9283, 9284, 9285, 9286, 9287, 9288, 9289, 9290, 9291, 9292, 9293, 9294, 9295, 9296, 9297, 9298, 9299, 9300, 9301, 9302, 9303, 9304, 9305, 9306, 9307, 9308, 9309, 9310, 9311, 9344, 9345, 9346, 9347, 9348, 9349, 9350, 9351, 9352, 9353, 9354, 9355, 9356, 9357, 9358, 9359, 9360, 9361, 9362, 9363, 9364, 9365, 9366, 9367, 9368, 9369, 9370, 9371, 9372, 9373, 9374, 9375, 9408, 9409, 9410, 9411, 9412, 9413, 9414, 9415, 9416, 9417, 9418, 9419, 9420, 9421, 9422, 9423, 9424, 9425, 9426, 9427, 9428, 9429, 9430, 9431, 9432, 9433, 9434, 9435, 9436, 9437, 9438, 9439, 10240, 10241, 10242, 10243, 10244, 10246, 10248, 10249, 10252, 10253, 10256, 10258, 10260, 10261, 10262, 10263, 10264, 10265, 10268, 10269, 10304, 10305, 10306, 10307, 10308, 10309, 10310, 10311, 10312, 10313, 10314, 10315, 10316, 10317, 10318, 10319, 10368, 10369, 10372, 10373, 10376, 10377, 10378, 10379, 10380, 10382, 10384, 10385, 10388, 10389, 10392, 10394, 10396, 10397, 10398, 10399, 10432, 10433, 10434, 10435, 10436, 10437, 10438, 10439, 10440, 10441, 10442, 10443, 10444, 10445, 10446, 10447, 10496, 10497, 10498, 10499, 10500, 10502, 10504, 10505, 10508, 10509, 10512, 10514, 10516, 10517, 10518, 10519, 10520, 10521, 10524, 10525, 10560, 10561, 10562, 10563, 10564, 10565, 10566, 10567, 10568, 10569, 10570, 10571, 10572, 10573, 10574, 10575, 10624, 10625, 10628, 10629, 10632, 10634, 10636, 10637, 10638, 10639, 10640, 10641, 10644, 10645, 10648, 10649, 10650, 10651, 10652, 10654, 10688, 10689, 10690, 10691, 10692, 10693, 10694, 10695, 10696, 10697, 10698, 10699, 10700, 10701, 10702, 10703, 11264, 11265, 11266, 11267, 11268, 11269, 11270, 11271, 11272, 11273, 11274, 11275, 11276, 11277, 11278, 11279, 11280, 11281, 11282, 11283, 11284, 11285, 11286, 11287, 11288, 11289, 11290, 11291, 11292, 11293, 11294, 11295, 11328, 11329, 11330, 11331, 11332, 11333, 11334, 11335, 11336, 11337, 11338, 11339, 11340, 11341, 11342, 11343, 11344, 11345, 11346, 11347, 11348, 11349, 11350, 11351, 11352, 11353, 11354, 11355, 11356, 11357, 11358, 11359, 11392, 11393, 11394, 11395, 11396, 11397, 11398, 11399, 11400, 11401, 11402, 11403, 11404, 11405, 11406, 11407, 11408, 11409, 11410, 11411, 11412, 11413, 11414, 11415, 11416, 11417, 11418, 11419, 11420, 11421, 11422, 11423, 11456, 11457, 11458, 11459, 11460, 11461, 11462, 11463, 11464, 11465, 11466, 11467, 11468, 11469, 11470, 11471, 11472, 11473, 11474, 11475, 11476, 11477, 11478, 11479, 11480, 11481, 11482, 11483, 11484, 11485, 11486, 11487, 16384, 16385, 16386, 16388, 16389, 16390, 16392, 16393, 16394, 16395, 16400, 16401, 16402, 16404, 16405, 16406, 16408, 16409, 16410, 16411, 16416, 16417, 16418, 16419, 16420, 16421, 16422, 16423, 16424, 16425, 16426, 16427, 16428, 16429, 16430, 16431, 16512, 16513, 16514, 16516, 16517, 16518, 16520, 16521, 16522, 16523, 16528, 16529, 16530, 16532, 16533, 16534, 16536, 16537, 16538, 16539, 16544, 16545, 16546, 16547, 16548, 16549, 16550, 16551, 16552, 16553, 16554, 16555, 16556, 16557, 16558, 16559, 16640, 16641, 16642, 16644, 16645, 16646, 16648, 16649, 16650, 16651, 16656, 16657, 16658, 16660, 16661, 16662, 16664, 16665, 16666, 16667, 16672, 16673, 16674, 16675, 16676, 16677, 16678, 16679, 16680, 16681, 16682, 16683, 16684, 16685, 16686, 16687, 16768, 16770, 16771, 16772, 16774, 16775, 16776, 16777, 16778, 16779, 16784, 16786, 16787, 16788, 16790, 16791, 16792, 16793, 16794, 16795, 16800, 16801, 16802, 16803, 16804, 16805, 16806, 16807, 16808, 16809, 16810, 16811, 16812, 16813, 16814, 16815, 16896, 16897, 16898, 16899, 16900, 16901, 16902, 16903, 16904, 16905, 16906, 16907, 16908, 16909, 16910, 16911, 16912, 16913, 16914, 16915, 16916, 16917, 16918, 16919, 16920, 16921, 16922, 16923, 16924, 16925, 16926, 16927, 16928, 16929, 16930, 16931, 16932, 16933, 16934, 16935, 16936, 16937, 16938, 16939, 16940, 16941, 16942, 16943, 16944, 16945, 16946, 16947, 16948, 16949, 16950, 16951, 16952, 16953, 16954, 16955, 16956, 16957, 16958, 16959, 17024, 17025, 17026, 17027, 17028, 17029, 17030, 17031, 17032, 17033, 17034, 17035, 17036, 17037, 17038, 17039, 17040, 17041, 17042, 17043, 17044, 17045, 17046, 17047, 17048, 17049, 17050, 17051, 17052, 17053, 17054, 17055, 17056, 17057, 17058, 17059, 17060, 17061, 17062, 17063, 17064, 17065, 17066, 17067, 17068, 17069, 17070, 17071, 17072, 17073, 17074, 17075, 17076, 17077, 17078, 17079, 17080, 17081, 17082, 17083, 17084, 17085, 17086, 17087, 18432, 18433, 18434, 18436, 18437, 18438, 18440, 18441, 18442, 18443, 18448, 18450, 18451, 18452, 18454, 18455, 18456, 18457, 18458, 18459, 18464, 18465, 18466, 18467, 18468, 18469, 18470, 18471, 18472, 18473, 18474, 18475, 18476, 18477, 18478, 18479, 18560, 18561, 18562, 18563, 18568, 18569, 18570, 18572, 18573, 18574, 18576, 18577, 18578, 18579, 18584, 18586, 18587, 18588, 18590, 18591, 18592, 18593, 18594, 18595, 18596, 18597, 18598, 18599, 18600, 18601, 18602, 18603, 18604, 18605, 18606, 18607, 18688, 18689, 18690, 18692, 18693, 18694, 18696, 18697, 18698, 18699, 18704, 18706, 18707, 18708, 18710, 18711, 18712, 18713, 18714, 18715, 18720, 18721, 18722, 18723, 18724, 18725, 18726, 18727, 18728, 18729, 18730, 18731, 18732, 18733, 18734, 18735, 18816, 18817, 18818, 18819, 18824, 18826, 18827, 18828, 18830, 18831, 18832, 18833, 18834, 18835, 18840, 18841, 18842, 18844, 18845, 18846, 18848, 18849, 18850, 18851, 18852, 18853, 18854, 18855, 18856, 18857, 18858, 18859, 18860, 18861, 18862, 18863, 18944, 18945, 18946, 18947, 18948, 18949, 18950, 18951, 18952, 18953, 18954, 18955, 18956, 18957, 18958, 18959, 18960, 18961, 18962, 18963, 18964, 18965, 18966, 18967, 18968, 18969, 18970, 18971, 18972, 18973, 18974, 18975, 18976, 18977, 18978, 18979, 18980, 18981, 18982, 18983, 18984, 18985, 18986, 18987, 18988, 18989, 18990, 18991, 18992, 18993, 18994, 18995, 18996, 18997, 18998, 18999, 19000, 19001, 19002, 19003, 19004, 19005, 19006, 19007, 19072, 19073, 19074, 19075, 19076, 19077, 19078, 19079, 19080, 19081, 19082, 19083, 19084, 19085, 19086, 19087, 19088, 19089, 19090, 19091, 19092, 19093, 19094, 19095, 19096, 19097, 19098, 19099, 19100, 19101, 19102, 19103, 19104, 19105, 19106, 19107, 19108, 19109, 19110, 19111, 19112, 19113, 19114, 19115, 19116, 19117, 19118, 19119, 19120, 19121, 19122, 19123, 19124, 19125, 19126, 19127, 19128, 19129, 19130, 19131, 19132, 19133, 19134, 19135, 24576, 24577, 24578, 24580, 24582, 24583, 24584, 24585, 24586, 24587, 24592, 24593, 24594, 24596, 24598, 24599, 24600, 24601, 24602, 24603, 24608, 24609, 24610, 24611, 24612, 24613, 24614, 24615, 24616, 24617, 24618, 24619, 24620, 24621, 24622, 24623, 24704, 24705, 24706, 24707, 24708, 24709, 24710, 24711, 24712, 24713, 24714, 24715, 24716, 24717, 24718, 24719, 24736, 24737, 24738, 24740, 24742, 24743, 24744, 24745, 24746, 24747, 24752, 24753, 24754, 24756, 24758, 24759, 24760, 24761, 24762, 24763, 24832, 24833, 24834, 24836, 24838, 24839, 24840, 24841, 24842, 24843, 24848, 24849, 24850, 24852, 24854, 24855, 24856, 24857, 24858, 24859, 24864, 24865, 24866, 24867, 24868, 24869, 24870, 24871, 24872, 24873, 24874, 24875, 24876, 24877, 24878, 24879, 24960, 24961, 24962, 24963, 24964, 24965, 24966, 24967, 24968, 24969, 24970, 24971, 24972, 24973, 24974, 24975, 24992, 24994, 24995, 24996, 24997, 24998, 25000, 25001, 25002, 25003, 25008, 25010, 25011, 25012, 25013, 25014, 25016, 25017, 25018, 25019, 25088, 25089, 25090, 25091, 25092, 25093, 25094, 25095, 25096, 25097, 25098, 25099, 25100, 25101, 25102, 25103, 25104, 25105, 25106, 25107, 25108, 25109, 25110, 25111, 25112, 25113, 25114, 25115, 25116, 25117, 25118, 25119, 25120, 25121, 25122, 25123, 25124, 25125, 25126, 25127, 25128, 25129, 25130, 25131, 25132, 25133, 25134, 25135, 25136, 25137, 25138, 25139, 25140, 25141, 25142, 25143, 25144, 25145, 25146, 25147, 25148, 25149, 25150, 25151, 25216, 25217, 25218, 25219, 25220, 25221, 25222, 25223, 25224, 25225, 25226, 25227, 25228, 25229, 25230, 25231, 25232, 25233, 25234, 25235, 25236, 25237, 25238, 25239, 25240, 25241, 25242, 25243, 25244, 25245, 25246, 25247, 25248, 25249, 25250, 25251, 25252, 25253, 25254, 25255, 25256, 25257, 25258, 25259, 25260, 25261, 25262, 25263, 25264, 25265, 25266, 25267, 25268, 25269, 25270, 25271, 25272, 25273, 25274, 25275, 25276, 25277, 25278, 25279, 26624, 26625, 26626, 26627, 26628, 26629, 26630, 26631, 26632, 26633, 26634, 26635, 26636, 26637, 26638, 26639, 26640, 26641, 26642, 26643, 26644, 26645, 26646, 26647, 26648, 26649, 26650, 26651, 26652, 26653, 26654, 26655, 26656, 26657, 26658, 26659, 26660, 26661, 26662, 26663, 26664, 26665, 26666, 26667, 26668, 26669, 26670, 26671, 26672, 26673, 26674, 26675, 26676, 26677, 26678, 26679, 26680, 26681, 26682, 26683, 26684, 26685, 26686, 26687, 26752, 26753, 26754, 26755, 26756, 26757, 26758, 26759, 26760, 26761, 26762, 26763, 26764, 26765, 26766, 26767, 26768, 26769, 26770, 26771, 26772, 26773, 26774, 26775, 26776, 26777, 26778, 26779, 26780, 26781, 26782, 26783, 26784, 26785, 26786, 26787, 26788, 26789, 26790, 26791, 26792, 26793, 26794, 26795, 26796, 26797, 26798, 26799, 26800, 26801, 26802, 26803, 26804, 26805, 26806, 26807, 26808, 26809, 26810, 26811, 26812, 26813, 26814, 26815, 27136, 27137, 27138, 27140, 27142, 27143, 27144, 27145, 27146, 27147, 27152, 27154, 27155, 27156, 27157, 27158, 27160, 27161, 27162, 27163, 27168, 27169, 27170, 27171, 27172, 27173, 27174, 27175, 27176, 27177, 27178, 27179, 27180, 27181, 27182, 27183, 27264, 27265, 27266, 27267, 27268, 27269, 27270, 27271, 27272, 27273, 27274, 27275, 27276, 27277, 27278, 27279, 27296, 27297, 27298, 27299, 27304, 27306, 27307, 27308, 27309, 27310, 27312, 27313, 27314, 27315, 27320, 27321, 27322, 27324, 27326, 27327, 27392, 27393, 27394, 27396, 27398, 27399, 27400, 27401, 27402, 27403, 27408, 27410, 27411, 27412, 27413, 27414, 27416, 27417, 27418, 27419, 27424, 27425, 27426, 27427, 27428, 27429, 27430, 27431, 27432, 27433, 27434, 27435, 27436, 27437, 27438, 27439, 27520, 27521, 27522, 27523, 27524, 27525, 27526, 27527, 27528, 27529, 27530, 27531, 27532, 27533, 27534, 27535, 27552, 27553, 27554, 27555, 27560, 27561, 27562, 27564, 27566, 27567, 27568, 27569, 27570, 27571, 27576, 27578, 27579, 27580, 27581, 27582, 32768, 32769, 32770, 32771, 32772, 32773, 32774, 32775, 32776, 32777, 32778, 32779, 32780, 32781, 32782, 32783, 32784, 32785, 32786, 32787, 32788, 32789, 32790, 32791, 32792, 32793, 32794, 32795, 32796, 32797, 32798, 32799, 32800, 32801, 32802, 32803, 32804, 32805, 32806, 32807, 32808, 32809, 32810, 32811, 32812, 32813, 32814, 32815, 32816, 32817, 32818, 32819, 32820, 32821, 32822, 32823, 32824, 32825, 32826, 32827, 32828, 32829, 32830, 32831, 32832, 32833, 32834, 32835, 32836, 32837, 32838, 32839, 32840, 32841, 32842, 32843, 32844, 32845, 32846, 32847, 32848, 32849, 32850, 32851, 32852, 32853, 32854, 32855, 32856, 32857, 32858, 32859, 32860, 32861, 32862, 32863, 32864, 32865, 32866, 32867, 32868, 32869, 32870, 32871, 32872, 32873, 32874, 32875, 32876, 32877, 32878, 32879, 32880, 32881, 32882, 32883, 32884, 32885, 32886, 32887, 32888, 32889, 32890, 32891, 32892, 32893, 32894, 32895, 33024, 33025, 33026, 33027, 33028, 33029, 33030, 33031, 33032, 33033, 33034, 33035, 33036, 33037, 33038, 33039, 33040, 33041, 33042, 33043, 33044, 33045, 33046, 33047, 33048, 33049, 33050, 33051, 33052, 33053, 33054, 33055, 33056, 33057, 33058, 33059, 33060, 33061, 33062, 33063, 33064, 33065, 33066, 33067, 33068, 33069, 33070, 33071, 33072, 33073, 33074, 33075, 33076, 33077, 33078, 33079, 33080, 33081, 33082, 33083, 33084, 33085, 33086, 33087, 33088, 33089, 33090, 33091, 33092, 33093, 33094, 33095, 33096, 33097, 33098, 33099, 33100, 33101, 33102, 33103, 33104, 33105, 33106, 33107, 33108, 33109, 33110, 33111, 33112, 33113, 33114, 33115, 33116, 33117, 33118, 33119, 33120, 33121, 33122, 33123, 33124, 33125, 33126, 33127, 33128, 33129, 33130, 33131, 33132, 33133, 33134, 33135, 33136, 33137, 33138, 33139, 33140, 33141, 33142, 33143, 33144, 33145, 33146, 33147, 33148, 33149, 33150, 33151, 33280, 33281, 33282, 33283, 33284, 33285, 33286, 33287, 33288, 33289, 33290, 33291, 33292, 33293, 33294, 33295, 33296, 33297, 33298, 33299, 33300, 33301, 33302, 33303, 33304, 33305, 33306, 33307, 33308, 33309, 33310, 33311, 33312, 33313, 33314, 33315, 33316, 33317, 33318, 33319, 33320, 33321, 33322, 33323, 33324, 33325, 33326, 33327, 33328, 33329, 33330, 33331, 33332, 33333, 33334, 33335, 33336, 33337, 33338, 33339, 33340, 33341, 33342, 33343, 33344, 33345, 33346, 33347, 33348, 33349, 33350, 33351, 33352, 33353, 33354, 33355, 33356, 33357, 33358, 33359, 33360, 33361, 33362, 33363, 33364, 33365, 33366, 33367, 33368, 33369, 33370, 33371, 33372, 33373, 33374, 33375, 33376, 33377, 33378, 33379, 33380, 33381, 33382, 33383, 33384, 33385, 33386, 33387, 33388, 33389, 33390, 33391, 33392, 33393, 33394, 33395, 33396, 33397, 33398, 33399, 33400, 33401, 33402, 33403, 33404, 33405, 33406, 33407, 33536, 33537, 33538, 33539, 33540, 33541, 33542, 33543, 33544, 33545, 33546, 33547, 33548, 33549, 33550, 33551, 33552, 33553, 33554, 33555, 33556, 33557, 33558, 33559, 33560, 33561, 33562, 33563, 33564, 33565, 33566, 33567, 33568, 33569, 33570, 33571, 33572, 33573, 33574, 33575, 33576, 33577, 33578, 33579, 33580, 33581, 33582, 33583, 33584, 33585, 33586, 33587, 33588, 33589, 33590, 33591, 33592, 33593, 33594, 33595, 33596, 33597, 33598, 33599, 33600, 33601, 33602, 33603, 33604, 33605, 33606, 33607, 33608, 33609, 33610, 33611, 33612, 33613, 33614, 33615, 33616, 33617, 33618, 33619, 33620, 33621, 33622, 33623, 33624, 33625, 33626, 33627, 33628, 33629, 33630, 33631, 33632, 33633, 33634, 33635, 33636, 33637, 33638, 33639, 33640, 33641, 33642, 33643, 33644, 33645, 33646, 33647, 33648, 33649, 33650, 33651, 33652, 33653, 33654, 33655, 33656, 33657, 33658, 33659, 33660, 33661, 33662, 33663, 33792, 33793, 33794, 33795, 33796, 33797, 33798, 33799, 33800, 33801, 33802, 33803, 33804, 33805, 33806, 33807, 33808, 33809, 33810, 33811, 33812, 33813, 33814, 33815, 33816, 33817, 33818, 33819, 33820, 33821, 33822, 33823, 33824, 33825, 33826, 33827, 33828, 33829, 33830, 33831, 33832, 33833, 33834, 33835, 33836, 33837, 33838, 33839, 33840, 33841, 33842, 33843, 33844, 33845, 33846, 33847, 33848, 33849, 33850, 33851, 33852, 33853, 33854, 33855, 33856, 33857, 33858, 33859, 33860, 33861, 33862, 33863, 33864, 33865, 33866, 33867, 33868, 33869, 33870, 33871, 33872, 33873, 33874, 33875, 33876, 33877, 33878, 33879, 33880, 33881, 33882, 33883, 33884, 33885, 33886, 33887, 33888, 33889, 33890, 33891, 33892, 33893, 33894, 33895, 33896, 33897, 33898, 33899, 33900, 33901, 33902, 33903, 33904, 33905, 33906, 33907, 33908, 33909, 33910, 33911, 33912, 33913, 33914, 33915, 33916, 33917, 33918, 33919, 34048, 34049, 34050, 34051, 34052, 34053, 34054, 34055, 34056, 34057, 34058, 34059, 34060, 34061, 34062, 34063, 34064, 34065, 34066, 34067, 34068, 34069, 34070, 34071, 34072, 34073, 34074, 34075, 34076, 34077, 34078, 34079, 34080, 34081, 34082, 34083, 34084, 34085, 34086, 34087, 34088, 34089, 34090, 34091, 34092, 34093, 34094, 34095, 34096, 34097, 34098, 34099, 34100, 34101, 34102, 34103, 34104, 34105, 34106, 34107, 34108, 34109, 34110, 34111, 34112, 34113, 34114, 34115, 34116, 34117, 34118, 34119, 34120, 34121, 34122, 34123, 34124, 34125, 34126, 34127, 34128, 34129, 34130, 34131, 34132, 34133, 34134, 34135, 34136, 34137, 34138, 34139, 34140, 34141, 34142, 34143, 34144, 34145, 34146, 34147, 34148, 34149, 34150, 34151, 34152, 34153, 34154, 34155, 34156, 34157, 34158, 34159, 34160, 34161, 34162, 34163, 34164, 34165, 34166, 34167, 34168, 34169, 34170, 34171, 34172, 34173, 34174, 34175, 34304, 34305, 34306, 34307, 34308, 34309, 34310, 34311, 34312, 34313, 34314, 34315, 34316, 34317, 34318, 34319, 34320, 34321, 34322, 34323, 34324, 34325, 34326, 34327, 34328, 34329, 34330, 34331, 34332, 34333, 34334, 34335, 34336, 34337, 34338, 34339, 34340, 34341, 34342, 34343, 34344, 34345, 34346, 34347, 34348, 34349, 34350, 34351, 34352, 34353, 34354, 34355, 34356, 34357, 34358, 34359, 34360, 34361, 34362, 34363, 34364, 34365, 34366, 34367, 34368, 34369, 34370, 34371, 34372, 34373, 34374, 34375, 34376, 34377, 34378, 34379, 34380, 34381, 34382, 34383, 34384, 34385, 34386, 34387, 34388, 34389, 34390, 34391, 34392, 34393, 34394, 34395, 34396, 34397, 34398, 34399, 34400, 34401, 34402, 34403, 34404, 34405, 34406, 34407, 34408, 34409, 34410, 34411, 34412, 34413, 34414, 34415, 34416, 34417, 34418, 34419, 34420, 34421, 34422, 34423, 34424, 34425, 34426, 34427, 34428, 34429, 34430, 34431, 34560, 34561, 34562, 34563, 34564, 34565, 34566, 34567, 34568, 34569, 34570, 34571, 34572, 34573, 34574, 34575, 34576, 34577, 34578, 34579, 34580, 34581, 34582, 34583, 34584, 34585, 34586, 34587, 34588, 34589, 34590, 34591, 34592, 34593, 34594, 34595, 34596, 34597, 34598, 34599, 34600, 34601, 34602, 34603, 34604, 34605, 34606, 34607, 34608, 34609, 34610, 34611, 34612, 34613, 34614, 34615, 34616, 34617, 34618, 34619, 34620, 34621, 34622, 34623, 34624, 34625, 34626, 34627, 34628, 34629, 34630, 34631, 34632, 34633, 34634, 34635, 34636, 34637, 34638, 34639, 34640, 34641, 34642, 34643, 34644, 34645, 34646, 34647, 34648, 34649, 34650, 34651, 34652, 34653, 34654, 34655, 34656, 34657, 34658, 34659, 34660, 34661, 34662, 34663, 34664, 34665, 34666, 34667, 34668, 34669, 34670, 34671, 34672, 34673, 34674, 34675, 34676, 34677, 34678, 34679, 34680, 34681, 34682, 34683, 34684, 34685, 34686, 34687, 36864, 36865, 36866, 36867, 36868, 36869, 36870, 36871, 36872, 36873, 36874, 36875, 36876, 36877, 36878, 36879, 36880, 36881, 36882, 36883, 36884, 36885, 36886, 36887, 36888, 36889, 36890, 36891, 36892, 36893, 36894, 36895, 36896, 36897, 36898, 36899, 36900, 36901, 36902, 36903, 36904, 36905, 36906, 36907, 36908, 36909, 36910, 36911, 36912, 36913, 36914, 36915, 36916, 36917, 36918, 36919, 36920, 36921, 36922, 36923, 36924, 36925, 36926, 36927, 36928, 36929, 36930, 36931, 36932, 36933, 36934, 36935, 36936, 36937, 36938, 36939, 36940, 36941, 36942, 36943, 36944, 36945, 36946, 36947, 36948, 36949, 36950, 36951, 36952, 36953, 36954, 36955, 36956, 36957, 36958, 36959, 36960, 36961, 36962, 36963, 36964, 36965, 36966, 36967, 36968, 36969, 36970, 36971, 36972, 36973, 36974, 36975, 36976, 36977, 36978, 36979, 36980, 36981, 36982, 36983, 36984, 36985, 36986, 36987, 36988, 36989, 36990, 36991, 37120, 37121, 37122, 37123, 37124, 37125, 37126, 37127, 37128, 37129, 37130, 37131, 37132, 37133, 37134, 37135, 37136, 37137, 37138, 37139, 37140, 37141, 37142, 37143, 37144, 37145, 37146, 37147, 37148, 37149, 37150, 37151, 37152, 37153, 37154, 37155, 37156, 37157, 37158, 37159, 37160, 37161, 37162, 37163, 37164, 37165, 37166, 37167, 37168, 37169, 37170, 37171, 37172, 37173, 37174, 37175, 37176, 37177, 37178, 37179, 37180, 37181, 37182, 37183, 37184, 37185, 37186, 37187, 37188, 37189, 37190, 37191, 37192, 37193, 37194, 37195, 37196, 37197, 37198, 37199, 37200, 37201, 37202, 37203, 37204, 37205, 37206, 37207, 37208, 37209, 37210, 37211, 37212, 37213, 37214, 37215, 37216, 37217, 37218, 37219, 37220, 37221, 37222, 37223, 37224, 37225, 37226, 37227, 37228, 37229, 37230, 37231, 37232, 37233, 37234, 37235, 37236, 37237, 37238, 37239, 37240, 37241, 37242, 37243, 37244, 37245, 37246, 37247, 37376, 37377, 37378, 37379, 37380, 37381, 37382, 37383, 37384, 37385, 37386, 37387, 37388, 37389, 37390, 37391, 37392, 37393, 37394, 37395, 37396, 37397, 37398, 37399, 37400, 37401, 37402, 37403, 37404, 37405, 37406, 37407, 37408, 37409, 37410, 37411, 37412, 37413, 37414, 37415, 37416, 37417, 37418, 37419, 37420, 37421, 37422, 37423, 37424, 37425, 37426, 37427, 37428, 37429, 37430, 37431, 37432, 37433, 37434, 37435, 37436, 37437, 37438, 37439, 37440, 37441, 37442, 37443, 37444, 37445, 37446, 37447, 37448, 37449, 37450, 37451, 37452, 37453, 37454, 37455, 37456, 37457, 37458, 37459, 37460, 37461, 37462, 37463, 37464, 37465, 37466, 37467, 37468, 37469, 37470, 37471, 37472, 37473, 37474, 37475, 37476, 37477, 37478, 37479, 37480, 37481, 37482, 37483, 37484, 37485, 37486, 37487, 37488, 37489, 37490, 37491, 37492, 37493, 37494, 37495, 37496, 37497, 37498, 37499, 37500, 37501, 37502, 37503, 37632, 37633, 37634, 37635, 37636, 37637, 37638, 37639, 37640, 37641, 37642, 37643, 37644, 37645, 37646, 37647, 37648, 37649, 37650, 37651, 37652, 37653, 37654, 37655, 37656, 37657, 37658, 37659, 37660, 37661, 37662, 37663, 37664, 37665, 37666, 37667, 37668, 37669, 37670, 37671, 37672, 37673, 37674, 37675, 37676, 37677, 37678, 37679, 37680, 37681, 37682, 37683, 37684, 37685, 37686, 37687, 37688, 37689, 37690, 37691, 37692, 37693, 37694, 37695, 37696, 37697, 37698, 37699, 37700, 37701, 37702, 37703, 37704, 37705, 37706, 37707, 37708, 37709, 37710, 37711, 37712, 37713, 37714, 37715, 37716, 37717, 37718, 37719, 37720, 37721, 37722, 37723, 37724, 37725, 37726, 37727, 37728, 37729, 37730, 37731, 37732, 37733, 37734, 37735, 37736, 37737, 37738, 37739, 37740, 37741, 37742, 37743, 37744, 37745, 37746, 37747, 37748, 37749, 37750, 37751, 37752, 37753, 37754, 37755, 37756, 37757, 37758, 37759, 37888, 37889, 37890, 37891, 37892, 37893, 37894, 37895, 37896, 37897, 37898, 37899, 37900, 37901, 37902, 37903, 37904, 37905, 37906, 37907, 37908, 37909, 37910, 37911, 37912, 37913, 37914, 37915, 37916, 37917, 37918, 37919, 37920, 37921, 37922, 37923, 37924, 37925, 37926, 37927, 37928, 37929, 37930, 37931, 37932, 37933, 37934, 37935, 37936, 37937, 37938, 37939, 37940, 37941, 37942, 37943, 37944, 37945, 37946, 37947, 37948, 37949, 37950, 37951, 37952, 37953, 37954, 37955, 37956, 37957, 37958, 37959, 37960, 37961, 37962, 37963, 37964, 37965, 37966, 37967, 37968, 37969, 37970, 37971, 37972, 37973, 37974, 37975, 37976, 37977, 37978, 37979, 37980, 37981, 37982, 37983, 37984, 37985, 37986, 37987, 37988, 37989, 37990, 37991, 37992, 37993, 37994, 37995, 37996, 37997, 37998, 37999, 38000, 38001, 38002, 38003, 38004, 38005, 38006, 38007, 38008, 38009, 38010, 38011, 38012, 38013, 38014, 38015, 38144, 38145, 38146, 38147, 38148, 38149, 38150, 38151, 38152, 38153, 38154, 38155, 38156, 38157, 38158, 38159, 38160, 38161, 38162, 38163, 38164, 38165, 38166, 38167, 38168, 38169, 38170, 38171, 38172, 38173, 38174, 38175, 38176, 38177, 38178, 38179, 38180, 38181, 38182, 38183, 38184, 38185, 38186, 38187, 38188, 38189, 38190, 38191, 38192, 38193, 38194, 38195, 38196, 38197, 38198, 38199, 38200, 38201, 38202, 38203, 38204, 38205, 38206, 38207, 38208, 38209, 38210, 38211, 38212, 38213, 38214, 38215, 38216, 38217, 38218, 38219, 38220, 38221, 38222, 38223, 38224, 38225, 38226, 38227, 38228, 38229, 38230, 38231, 38232, 38233, 38234, 38235, 38236, 38237, 38238, 38239, 38240, 38241, 38242, 38243, 38244, 38245, 38246, 38247, 38248, 38249, 38250, 38251, 38252, 38253, 38254, 38255, 38256, 38257, 38258, 38259, 38260, 38261, 38262, 38263, 38264, 38265, 38266, 38267, 38268, 38269, 38270, 38271, 38400, 38401, 38402, 38403, 38404, 38405, 38406, 38407, 38408, 38409, 38410, 38411, 38412, 38413, 38414, 38415, 38416, 38417, 38418, 38419, 38420, 38421, 38422, 38423, 38424, 38425, 38426, 38427, 38428, 38429, 38430, 38431, 38432, 38433, 38434, 38435, 38436, 38437, 38438, 38439, 38440, 38441, 38442, 38443, 38444, 38445, 38446, 38447, 38448, 38449, 38450, 38451, 38452, 38453, 38454, 38455, 38456, 38457, 38458, 38459, 38460, 38461, 38462, 38463, 38464, 38465, 38466, 38467, 38468, 38469, 38470, 38471, 38472, 38473, 38474, 38475, 38476, 38477, 38478, 38479, 38480, 38481, 38482, 38483, 38484, 38485, 38486, 38487, 38488, 38489, 38490, 38491, 38492, 38493, 38494, 38495, 38496, 38497, 38498, 38499, 38500, 38501, 38502, 38503, 38504, 38505, 38506, 38507, 38508, 38509, 38510, 38511, 38512, 38513, 38514, 38515, 38516, 38517, 38518, 38519, 38520, 38521, 38522, 38523, 38524, 38525, 38526, 38527, 38656, 38657, 38658, 38659, 38660, 38661, 38662, 38663, 38664, 38665, 38666, 38667, 38668, 38669, 38670, 38671, 38672, 38673, 38674, 38675, 38676, 38677, 38678, 38679, 38680, 38681, 38682, 38683, 38684, 38685, 38686, 38687, 38688, 38689, 38690, 38691, 38692, 38693, 38694, 38695, 38696, 38697, 38698, 38699, 38700, 38701, 38702, 38703, 38704, 38705, 38706, 38707, 38708, 38709, 38710, 38711, 38712, 38713, 38714, 38715, 38716, 38717, 38718, 38719, 38720, 38721, 38722, 38723, 38724, 38725, 38726, 38727, 38728, 38729, 38730, 38731, 38732, 38733, 38734, 38735, 38736, 38737, 38738, 38739, 38740, 38741, 38742, 38743, 38744, 38745, 38746, 38747, 38748, 38749, 38750, 38751, 38752, 38753, 38754, 38755, 38756, 38757, 38758, 38759, 38760, 38761, 38762, 38763, 38764, 38765, 38766, 38767, 38768, 38769, 38770, 38771, 38772, 38773, 38774, 38775, 38776, 38777, 38778, 38779, 38780, 38781, 38782, 38783

splinters   TBA8

The length of the sequence for arity n is TBA7(n), the number of n-ary splinters.

| n |  | sequence

|
|

0  | 2  | 0, 1,
1  | 2  | 2, 3,
2  | 10  | 4, 5, 6, 7, 8, 9, 10, 11, 14, 15,
3  | 170  | 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 54, 55, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 84, 85, 86, 87, 90, 91, 94, 95, 96, 97, 98, 99, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 114, 115, 118, 119, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 184, 185, 186, 187, 188, 189, 190, 191, 194, 195, 200, 201, 206, 207, 212, 213, 216, 217, 222, 223, 224, 225, 232, 233, 234, 235, 236, 237, 238, 239, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255,
4  | 51380  | 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 306, 307, 310, 311, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 340, 341, 342, 343, 346, 347, 350, 351, 352, 353, 354, 355, 358, 359, 360, 361, 362, 363, 366, 367, 368, 369, 370, 371, 374, 375, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 440, 441, 442, 443, 444, 445, 446, 447, 450, 451, 456, 457, 462, 463, 468, 469, 472, 473, 478, 479, 480, 481, 488, 489, 490, 491, 492, 493, 494, 495, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 582, 583, 584, 585, 586, 587, 590, 591, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 626, 627, 628, 629, 630, 631, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 744, 745, 746, 747, 748, 749, 750, 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39702, 39703, 39704, 39705, 39706, 39707, 39708, 39709, 39710, 39711, 39728, 39729, 39730, 39731, 39732, 39733, 39734, 39735, 39736, 39737, 39738, 39739, 39740, 39741, 39742, 39743, 39744, 39745, 39750, 39751, 39752, 39753, 39758, 39759, 39760, 39761, 39762, 39763, 39764, 39765, 39766, 39767, 39768, 39769, 39770, 39771, 39772, 39773, 39774, 39775, 39776, 39777, 39778, 39779, 39780, 39781, 39782, 39783, 39784, 39785, 39786, 39787, 39788, 39789, 39790, 39791, 39792, 39793, 39794, 39795, 39796, 39797, 39798, 39799, 39800, 39801, 39802, 39803, 39804, 39805, 39806, 39807, 39808, 39809, 39810, 39811, 39812, 39813, 39814, 39815, 39816, 39817, 39818, 39819, 39820, 39821, 39822, 39823, 39824, 39825, 39826, 39827, 39828, 39829, 39830, 39831, 39832, 39833, 39834, 39835, 39836, 39837, 39838, 39839, 39840, 39841, 39842, 39843, 39844, 39845, 39846, 39847, 39848, 39849, 39850, 39851, 39852, 39853, 39854, 39855, 39856, 39857, 39858, 39859, 39860, 39861, 39862, 39863, 39864, 39865, 39866, 39867, 39868, 39869, 39870, 39871, 39872, 39873, 39874, 39875, 39876, 39877, 39878, 39879, 39880, 39881, 39882, 39883, 39884, 39885, 39886, 39887, 39888, 39889, 39890, 39891, 39892, 39893, 39894, 39895, 39896, 39897, 39898, 39899, 39900, 39901, 39902, 39903, 39904, 39905, 39906, 39907, 39908, 39909, 39910, 39911, 39912, 39913, 39914, 39915, 39916, 39917, 39918, 39919, 39920, 39921, 39922, 39923, 39924, 39925, 39926, 39927, 39928, 39929, 39930, 39931, 39932, 39933, 39934, 39935, 39936, 39937, 39938, 39939, 39940, 39941, 39942, 39943, 39944, 39945, 39946, 39947, 39948, 39949, 39950, 39951, 39952, 39953, 39954, 39955, 39956, 39957, 39958, 39959, 39960, 39961, 39962, 39963, 39964, 39965, 39966, 39967, 39968, 39969, 39970, 39971, 39972, 39973, 39974, 39975, 39976, 39977, 39978, 39979, 39980, 39981, 39982, 39983, 39984, 39985, 39990, 39991, 39992, 39993, 39998, 39999, 40000, 40001, 40002, 40003, 40004, 40005, 40006, 40007, 40008, 40009, 40010, 40011, 40012, 40013, 40014, 40015, 40032, 40033, 40034, 40035, 40036, 40037, 40038, 40039, 40040, 40041, 40042, 40043, 40044, 40045, 40046, 40047, 40048, 40049, 40050, 40051, 40052, 40053, 40054, 40055, 40056, 40057, 40058, 40059, 40060, 40061, 40062, 40063, 40064, 40065, 40066, 40067, 40068, 40069, 40070, 40071, 40072, 40073, 40074, 40075, 40076, 40077, 40078, 40079, 40080, 40081, 40082, 40083, 40084, 40085, 40086, 40087, 40088, 40089, 40090, 40091, 40092, 40093, 40094, 40095, 40096, 40097, 40098, 40099, 40100, 40101, 40102, 40103, 40104, 40105, 40106, 40107, 40108, 40109, 40110, 40111, 40112, 40113, 40114, 40115, 40116, 40117, 40118, 40119, 40120, 40121, 40122, 40123, 40124, 40125, 40126, 40127, 40128, 40129, 40130, 40131, 40132, 40133, 40134, 40135, 40136, 40137, 40138, 40139, 40140, 40141, 40142, 40143, 40144, 40145, 40146, 40147, 40148, 40149, 40150, 40151, 40152, 40153, 40154, 40155, 40156, 40157, 40158, 40159, 40160, 40161, 40162, 40163, 40164, 40165, 40166, 40167, 40168, 40169, 40170, 40171, 40172, 40173, 40174, 40175, 40176, 40177, 40178, 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40489, 40490, 40491, 40492, 40493, 40494, 40495, 40496, 40497, 40498, 40499, 40500, 40501, 40502, 40503, 40504, 40505, 40506, 40507, 40508, 40509, 40510, 40511, 40512, 40513, 40514, 40515, 40516, 40517, 40518, 40519, 40520, 40521, 40522, 40523, 40524, 40525, 40526, 40527, 40528, 40529, 40530, 40531, 40532, 40533, 40534, 40535, 40536, 40537, 40538, 40539, 40540, 40541, 40542, 40543, 40544, 40545, 40546, 40547, 40548, 40549, 40550, 40551, 40552, 40553, 40554, 40555, 40556, 40557, 40558, 40559, 40576, 40577, 40578, 40579, 40580, 40581, 40582, 40583, 40584, 40585, 40586, 40587, 40588, 40589, 40590, 40591, 40592, 40593, 40594, 40595, 40596, 40597, 40598, 40599, 40600, 40601, 40602, 40603, 40604, 40605, 40606, 40607, 40608, 40609, 40610, 40611, 40612, 40613, 40614, 40615, 40616, 40617, 40618, 40619, 40620, 40621, 40622, 40623, 40624, 40625, 40626, 40627, 40628, 40629, 40630, 40631, 40632, 40633, 40634, 40635, 40636, 40637, 40638, 40639, 40640, 40641, 40642, 40643, 40644, 40645, 40646, 40647, 40648, 40649, 40650, 40651, 40652, 40653, 40654, 40655, 40656, 40657, 40658, 40659, 40660, 40661, 40662, 40663, 40664, 40665, 40666, 40667, 40668, 40669, 40670, 40671, 40672, 40673, 40674, 40675, 40676, 40677, 40678, 40679, 40680, 40681, 40682, 40683, 40684, 40685, 40686, 40687, 40688, 40689, 40690, 40691, 40692, 40693, 40694, 40695, 40696, 40697, 40698, 40699, 40700, 40701, 40702, 40703, 40704, 40705, 40706, 40707, 40708, 40709, 40710, 40711, 40712, 40713, 40714, 40715, 40716, 40717, 40718, 40719, 40720, 40721, 40722, 40723, 40724, 40725, 40726, 40727, 40728, 40729, 40730, 40731, 40732, 40733, 40734, 40735, 40736, 40737, 40738, 40739, 40740, 40741, 40742, 40743, 40744, 40745, 40746, 40747, 40748, 40749, 40750, 40751, 40752, 40753, 40754, 40755, 40756, 40757, 40758, 40759, 40760, 40761, 40762, 40763, 40764, 40765, 40766, 40767, 40768, 40769, 40770, 40771, 40772, 40773, 40774, 40775, 40776, 40777, 40778, 40779, 40780, 40781, 40782, 40783, 40784, 40785, 40786, 40787, 40788, 40789, 40790, 40791, 40792, 40793, 40794, 40795, 40796, 40797, 40798, 40799, 40816, 40817, 40818, 40819, 40820, 40821, 40822, 40823, 40824, 40825, 40826, 40827, 40828, 40829, 40830, 40831, 40832, 40833, 40834, 40835, 40836, 40837, 40838, 40839, 40840, 40841, 40842, 40843, 40844, 40845, 40846, 40847, 40848, 40849, 40850, 40851, 40852, 40853, 40854, 40855, 40856, 40857, 40858, 40859, 40860, 40861, 40862, 40863, 40864, 40865, 40866, 40867, 40868, 40869, 40870, 40871, 40872, 40873, 40874, 40875, 40876, 40877, 40878, 40879, 40880, 40881, 40882, 40883, 40884, 40885, 40886, 40887, 40888, 40889, 40890, 40891, 40892, 40893, 40894, 40895, 40896, 40897, 40898, 40899, 40900, 40901, 40902, 40903, 40904, 40905, 40906, 40907, 40908, 40909, 40910, 40911, 40912, 40913, 40914, 40915, 40916, 40917, 40918, 40919, 40920, 40921, 40922, 40923, 40924, 40925, 40926, 40927, 40928, 40929, 40930, 40931, 40932, 40933, 40934, 40935, 40936, 40937, 40938, 40939, 40940, 40941, 40942, 40943, 40944, 40945, 40946, 40947, 40948, 40949, 40950, 40951, 40952, 40953, 40954, 40955, 40956, 40957, 40958, 40959, 40964, 40965, 40966, 40967, 40968, 40969, 40970, 40971, 40972, 40973, 40974, 40975, 40984, 40985, 40986, 40987, 40988, 40989, 40990, 40991, 40996, 40997, 40998, 40999, 41004, 41005, 41006, 41007, 41012, 41013, 41014, 41015, 41016, 41017, 41018, 41019, 41024, 41025, 41026, 41027, 41032, 41033, 41034, 41035, 41036, 41037, 41038, 41039, 41044, 41045, 41046, 41047, 41048, 41049, 41050, 41051, 41052, 41053, 41054, 41055, 41056, 41057, 41058, 41059, 41060, 41061, 41062, 41063, 41064, 41065, 41066, 41067, 41072, 41073, 41074, 41075, 41076, 41077, 41078, 41079, 41084, 41085, 41086, 41087, 41088, 41089, 41090, 41091, 41092, 41093, 41094, 41095, 41100, 41101, 41102, 41103, 41104, 41105, 41106, 41107, 41108, 41109, 41110, 41111, 41112, 41113, 41114, 41115, 41124, 41125, 41126, 41127, 41128, 41129, 41130, 41131, 41132, 41133, 41134, 41135, 41136, 41137, 41138, 41139, 41144, 41145, 41146, 41147, 41148, 41149, 41150, 41151, 41152, 41153, 41154, 41155, 41156, 41157, 41158, 41159, 41160, 41161, 41162, 41163, 41168, 41169, 41170, 41171, 41172, 41173, 41174, 41175, 41180, 41181, 41182, 41183, 41184, 41185, 41186, 41187, 41192, 41193, 41194, 41195, 41196, 41197, 41198, 41199, 41204, 41205, 41206, 41207, 41208, 41209, 41210, 41211, 41212, 41213, 41214, 41215, 41224, 41225, 41226, 41227, 41228, 41229, 41230, 41231, 41232, 41233, 41234, 41235, 41240, 41241, 41242, 41243, 41244, 41245, 41246, 41247, 41248, 41249, 41250, 41251, 41260, 41261, 41262, 41263, 41264, 41265, 41266, 41267, 41272, 41273, 41274, 41275, 41280, 41281, 41282, 41283, 41288, 41289, 41290, 41291, 41292, 41293, 41294, 41295, 41300, 41301, 41302, 41303, 41304, 41305, 41306, 41307, 41308, 41309, 41310, 41311, 41312, 41313, 41314, 41315, 41316, 41317, 41318, 41319, 41320, 41321, 41322, 41323, 41328, 41329, 41330, 41331, 41332, 41333, 41334, 41335, 41340, 41341, 41342, 41343, 41344, 41345, 41346, 41347, 41348, 41349, 41350, 41351, 41356, 41357, 41358, 41359, 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41569, 41572, 41573, 41574, 41575, 41576, 41577, 41578, 41579, 41586, 41587, 41588, 41589, 41590, 41591, 41596, 41597, 41598, 41599, 41600, 41601, 41602, 41603, 41604, 41605, 41606, 41607, 41612, 41613, 41614, 41615, 41616, 41617, 41618, 41619, 41620, 41621, 41622, 41623, 41624, 41625, 41626, 41627, 41636, 41637, 41638, 41639, 41640, 41641, 41642, 41643, 41644, 41645, 41646, 41647, 41648, 41649, 41650, 41651, 41656, 41657, 41658, 41659, 41660, 41661, 41662, 41663, 41664, 41665, 41666, 41667, 41668, 41669, 41670, 41671, 41672, 41673, 41674, 41675, 41680, 41681, 41682, 41683, 41684, 41685, 41686, 41687, 41692, 41693, 41694, 41695, 41696, 41697, 41698, 41699, 41704, 41705, 41706, 41707, 41708, 41709, 41710, 41711, 41716, 41717, 41718, 41719, 41720, 41721, 41722, 41723, 41724, 41725, 41726, 41727, 41732, 41733, 41734, 41735, 41736, 41737, 41738, 41739, 41744, 41745, 41746, 41747, 41752, 41753, 41754, 41755, 41760, 41761, 41762, 41763, 41764, 41765, 41766, 41767, 41776, 41777, 41778, 41779, 41780, 41781, 41782, 41783, 41784, 41785, 41786, 41787, 41792, 41793, 41794, 41795, 41800, 41801, 41802, 41803, 41804, 41805, 41806, 41807, 41814, 41815, 41816, 41817, 41818, 41819, 41820, 41821, 41822, 41823, 41824, 41825, 41826, 41827, 41828, 41829, 41832, 41833, 41834, 41835, 41840, 41841, 41842, 41843, 41846, 41847, 41852, 41853, 41854, 41855, 41856, 41857, 41858, 41859, 41860, 41861, 41862, 41863, 41868, 41869, 41870, 41871, 41872, 41873, 41874, 41875, 41876, 41877, 41878, 41879, 41880, 41881, 41882, 41883, 41892, 41893, 41894, 41895, 41896, 41897, 41898, 41899, 41900, 41901, 41902, 41903, 41904, 41905, 41906, 41907, 41912, 41913, 41914, 41915, 41916, 41917, 41918, 41919, 41920, 41921, 41922, 41923, 41924, 41925, 41926, 41927, 41928, 41929, 41930, 41931, 41936, 41937, 41938, 41939, 41940, 41941, 41942, 41943, 41948, 41949, 41950, 41951, 41952, 41953, 41954, 41955, 41960, 41961, 41962, 41963, 41964, 41965, 41966, 41967, 41972, 41973, 41974, 41975, 41976, 41977, 41978, 41979, 41980, 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63170, 63171, 63172, 63173, 63176, 63177, 63178, 63179, 63180, 63181, 63182, 63183, 63184, 63185, 63188, 63189, 63190, 63191, 63192, 63193, 63194, 63195, 63196, 63197, 63198, 63199, 63200, 63201, 63202, 63203, 63204, 63205, 63206, 63207, 63208, 63209, 63210, 63211, 63212, 63213, 63214, 63215, 63216, 63217, 63218, 63219, 63220, 63221, 63222, 63223, 63224, 63225, 63226, 63227, 63228, 63229, 63230, 63231, 63232, 63233, 63234, 63235, 63236, 63237, 63238, 63239, 63246, 63247, 63248, 63249, 63250, 63251, 63252, 63253, 63254, 63255, 63262, 63263, 63264, 63265, 63266, 63267, 63268, 63269, 63276, 63277, 63278, 63279, 63280, 63281, 63284, 63285, 63286, 63287, 63292, 63293, 63294, 63295, 63296, 63297, 63298, 63299, 63300, 63301, 63306, 63307, 63310, 63311, 63312, 63313, 63314, 63315, 63318, 63319, 63322, 63323, 63326, 63327, 63328, 63329, 63334, 63335, 63336, 63337, 63338, 63339, 63340, 63341, 63342, 63343, 63344, 63345, 63346, 63347, 63348, 63349, 63352, 63353, 63354, 63355, 63356, 63357, 63358, 63359, 63362, 63363, 63364, 63365, 63366, 63367, 63368, 63369, 63370, 63371, 63372, 63373, 63374, 63375, 63376, 63377, 63382, 63383, 63384, 63385, 63386, 63387, 63388, 63389, 63390, 63391, 63392, 63393, 63396, 63397, 63398, 63399, 63400, 63401, 63402, 63403, 63404, 63405, 63406, 63407, 63410, 63411, 63412, 63413, 63414, 63415, 63416, 63417, 63418, 63419, 63420, 63421, 63422, 63423, 63424, 63425, 63426, 63427, 63430, 63431, 63432, 63433, 63434, 63435, 63436, 63437, 63438, 63439, 63442, 63443, 63444, 63445, 63446, 63447, 63448, 63449, 63450, 63451, 63452, 63453, 63454, 63455, 63456, 63457, 63458, 63459, 63460, 63461, 63462, 63463, 63464, 63465, 63466, 63467, 63468, 63469, 63470, 63471, 63472, 63473, 63474, 63475, 63476, 63477, 63478, 63479, 63480, 63481, 63482, 63483, 63484, 63485, 63486, 63487, 63488, 63489, 63490, 63491, 63492, 63493, 63494, 63495, 63502, 63503, 63504, 63505, 63506, 63507, 63508, 63509, 63510, 63511, 63518, 63519, 63520, 63521, 63522, 63523, 63526, 63527, 63532, 63533, 63534, 63535, 63538, 63539, 63540, 63541, 63542, 63543, 63548, 63549, 63550, 63551, 63552, 63553, 63556, 63557, 63558, 63559, 63562, 63563, 63566, 63567, 63570, 63571, 63572, 63573, 63574, 63575, 63578, 63579, 63582, 63583, 63584, 63585, 63590, 63591, 63592, 63593, 63594, 63595, 63596, 63597, 63598, 63599, 63616, 63617, 63618, 63619, 63620, 63621, 63622, 63623, 63624, 63625, 63626, 63627, 63628, 63629, 63630, 63631, 63632, 63633, 63634, 63635, 63636, 63637, 63638, 63639, 63640, 63641, 63642, 63643, 63644, 63645, 63646, 63647, 63648, 63649, 63650, 63651, 63652, 63653, 63654, 63655, 63656, 63657, 63658, 63659, 63660, 63661, 63662, 63663, 63664, 63665, 63666, 63667, 63668, 63669, 63670, 63671, 63672, 63673, 63674, 63675, 63676, 63677, 63678, 63679, 63680, 63681, 63682, 63683, 63684, 63685, 63686, 63687, 63688, 63689, 63690, 63691, 63692, 63693, 63694, 63695, 63696, 63697, 63698, 63699, 63700, 63701, 63702, 63703, 63704, 63705, 63706, 63707, 63708, 63709, 63710, 63711, 63712, 63713, 63714, 63715, 63716, 63717, 63718, 63719, 63720, 63721, 63722, 63723, 63724, 63725, 63726, 63727, 63728, 63729, 63730, 63731, 63732, 63733, 63734, 63735, 63736, 63737, 63738, 63739, 63740, 63741, 63742, 63743, 63744, 63745, 63746, 63747, 63748, 63749, 63750, 63751, 63752, 63753, 63760, 63761, 63762, 63763, 63764, 63765, 63766, 63767, 63768, 63769, 63776, 63777, 63778, 63779, 63780, 63781, 63784, 63785, 63786, 63787, 63792, 63793, 63796, 63797, 63798, 63799, 63800, 63801, 63802, 63803, 63808, 63809, 63810, 63811, 63812, 63813, 63816, 63817, 63820, 63821, 63824, 63825, 63826, 63827, 63830, 63831, 63832, 63833, 63836, 63837, 63856, 63857, 63862, 63863, 63864, 63865, 63866, 63867, 63868, 63869, 63870, 63871, 63872, 63873, 63874, 63875, 63876, 63877, 63878, 63879, 63880, 63881, 63882, 63883, 63884, 63885, 63886, 63887, 63888, 63889, 63890, 63891, 63892, 63893, 63894, 63895, 63896, 63897, 63898, 63899, 63900, 63901, 63902, 63903, 63904, 63905, 63906, 63907, 63908, 63909, 63910, 63911, 63912, 63913, 63914, 63915, 63916, 63917, 63918, 63919, 63920, 63921, 63922, 63923, 63924, 63925, 63926, 63927, 63928, 63929, 63930, 63931, 63932, 63933, 63934, 63935, 63936, 63937, 63938, 63939, 63940, 63941, 63942, 63943, 63944, 63945, 63946, 63947, 63948, 63949, 63950, 63951, 63952, 63953, 63954, 63955, 63956, 63957, 63958, 63959, 63960, 63961, 63962, 63963, 63964, 63965, 63966, 63967, 63968, 63969, 63970, 63971, 63972, 63973, 63974, 63975, 63976, 63977, 63978, 63979, 63980, 63981, 63982, 63983, 63984, 63985, 63986, 63987, 63988, 63989, 63990, 63991, 63992, 63993, 63994, 63995, 63996, 63997, 63998, 63999, 64004, 64005, 64006, 64007, 64008, 64009, 64012, 64013, 64020, 64021, 64022, 64023, 64024, 64025, 64028, 64029, 64036, 64037, 64040, 64041, 64042, 64043, 64044, 64045, 64046, 64047, 64054, 64055, 64056, 64057, 64062, 64063, 64064, 64065, 64066, 64067, 64068, 64069, 64070, 64071, 64072, 64073, 64076, 64077, 64096, 64097, 64098, 64099, 64100, 64101, 64104, 64105, 64106, 64107, 64108, 64109, 64110, 64111, 64112, 64113, 64116, 64117, 64118, 64119, 64120, 64121, 64122, 64123, 64124, 64125, 64126, 64127, 64128, 64129, 64130, 64131, 64132, 64133, 64134, 64135, 64136, 64137, 64138, 64139, 64140, 64141, 64142, 64143, 64144, 64145, 64146, 64147, 64148, 64149, 64150, 64151, 64152, 64153, 64154, 64155, 64156, 64157, 64158, 64159, 64160, 64161, 64162, 64163, 64164, 64165, 64166, 64167, 64168, 64169, 64170, 64171, 64172, 64173, 64174, 64175, 64176, 64177, 64178, 64179, 64180, 64181, 64182, 64183, 64184, 64185, 64186, 64187, 64188, 64189, 64190, 64191, 64192, 64193, 64194, 64195, 64196, 64197, 64198, 64199, 64200, 64201, 64202, 64203, 64204, 64205, 64206, 64207, 64208, 64209, 64210, 64211, 64212, 64213, 64214, 64215, 64216, 64217, 64218, 64219, 64220, 64221, 64222, 64223, 64224, 64225, 64226, 64227, 64228, 64229, 64230, 64231, 64232, 64233, 64234, 64235, 64236, 64237, 64238, 64239, 64240, 64241, 64242, 64243, 64244, 64245, 64246, 64247, 64248, 64249, 64250, 64251, 64252, 64253, 64254, 64255, 64256, 64257, 64258, 64259, 64266, 64267, 64270, 64271, 64272, 64273, 64274, 64275, 64282, 64283, 64286, 64287, 64288, 64289, 64296, 64297, 64302, 64303, 64306, 64307, 64312, 64313, 64314, 64315, 64316, 64317, 64318, 64319, 64336, 64337, 64338, 64339, 64340, 64341, 64342, 64343, 64346, 64347, 64350, 64351, 64352, 64353, 64354, 64355, 64358, 64359, 64360, 64361, 64362, 64363, 64364, 64365, 64366, 64367, 64370, 64371, 64372, 64373, 64374, 64375, 64376, 64377, 64378, 64379, 64380, 64381, 64382, 64383, 64384, 64385, 64386, 64387, 64388, 64389, 64390, 64391, 64392, 64393, 64394, 64395, 64396, 64397, 64398, 64399, 64400, 64401, 64402, 64403, 64404, 64405, 64406, 64407, 64408, 64409, 64410, 64411, 64412, 64413, 64414, 64415, 64416, 64417, 64418, 64419, 64420, 64421, 64422, 64423, 64424, 64425, 64426, 64427, 64428, 64429, 64430, 64431, 64432, 64433, 64434, 64435, 64436, 64437, 64438, 64439, 64440, 64441, 64442, 64443, 64444, 64445, 64446, 64447, 64448, 64449, 64450, 64451, 64452, 64453, 64454, 64455, 64456, 64457, 64458, 64459, 64460, 64461, 64462, 64463, 64464, 64465, 64466, 64467, 64468, 64469, 64470, 64471, 64472, 64473, 64474, 64475, 64476, 64477, 64478, 64479, 64480, 64481, 64482, 64483, 64484, 64485, 64486, 64487, 64488, 64489, 64490, 64491, 64492, 64493, 64494, 64495, 64496, 64497, 64498, 64499, 64500, 64501, 64502, 64503, 64504, 64505, 64506, 64507, 64508, 64509, 64510, 64511, 64514, 64515, 64518, 64519, 64520, 64521, 64522, 64523, 64530, 64531, 64534, 64535, 64536, 64537, 64538, 64539, 64544, 64545, 64546, 64547, 64548, 64549, 64550, 64551, 64552, 64553, 64554, 64555, 64578, 64579, 64584, 64585, 64586, 64587, 64588, 64589, 64590, 64591, 64598, 64599, 64600, 64601, 64606, 64607, 64608, 64609, 64610, 64611, 64612, 64613, 64616, 64617, 64618, 64619, 64620, 64621, 64622, 64623, 64624, 64625, 64626, 64627, 64630, 64631, 64632, 64633, 64634, 64635, 64636, 64637, 64638, 64639, 64640, 64641, 64642, 64643, 64644, 64645, 64646, 64647, 64648, 64649, 64650, 64651, 64652, 64653, 64654, 64655, 64656, 64657, 64658, 64659, 64660, 64661, 64662, 64663, 64664, 64665, 64666, 64667, 64668, 64669, 64670, 64671, 64672, 64673, 64674, 64675, 64676, 64677, 64678, 64679, 64680, 64681, 64682, 64683, 64684, 64685, 64686, 64687, 64688, 64689, 64690, 64691, 64692, 64693, 64694, 64695, 64696, 64697, 64698, 64699, 64700, 64701, 64702, 64703, 64704, 64705, 64706, 64707, 64708, 64709, 64710, 64711, 64712, 64713, 64714, 64715, 64716, 64717, 64718, 64719, 64720, 64721, 64722, 64723, 64724, 64725, 64726, 64727, 64728, 64729, 64730, 64731, 64732, 64733, 64734, 64735, 64736, 64737, 64738, 64739, 64740, 64741, 64742, 64743, 64744, 64745, 64746, 64747, 64748, 64749, 64750, 64751, 64752, 64753, 64754, 64755, 64756, 64757, 64758, 64759, 64760, 64761, 64762, 64763, 64764, 64765, 64766, 64767, 64768, 64769, 64772, 64773, 64780, 64781, 64782, 64783, 64784, 64785, 64788, 64789, 64796, 64797, 64798, 64799, 64816, 64817, 64818, 64819, 64820, 64821, 64822, 64823, 64828, 64829, 64830, 64831, 64832, 64833, 64840, 64841, 64846, 64847, 64852, 64853, 64856, 64857, 64858, 64859, 64860, 64861, 64862, 64863, 64864, 64865, 64868, 64869, 64870, 64871, 64872, 64873, 64874, 64875, 64876, 64877, 64878, 64879, 64882, 64883, 64884, 64885, 64886, 64887, 64888, 64889, 64890, 64891, 64892, 64893, 64894, 64895, 64896, 64897, 64898, 64899, 64900, 64901, 64902, 64903, 64904, 64905, 64906, 64907, 64908, 64909, 64910, 64911, 64912, 64913, 64914, 64915, 64916, 64917, 64918, 64919, 64920, 64921, 64922, 64923, 64924, 64925, 64926, 64927, 64928, 64929, 64930, 64931, 64932, 64933, 64934, 64935, 64936, 64937, 64938, 64939, 64940, 64941, 64942, 64943, 64944, 64945, 64946, 64947, 64948, 64949, 64950, 64951, 64952, 64953, 64954, 64955, 64956, 64957, 64958, 64959, 64960, 64961, 64962, 64963, 64964, 64965, 64966, 64967, 64968, 64969, 64970, 64971, 64972, 64973, 64974, 64975, 64976, 64977, 64978, 64979, 64980, 64981, 64982, 64983, 64984, 64985, 64986, 64987, 64988, 64989, 64990, 64991, 64992, 64993, 64994, 64995, 64996, 64997, 64998, 64999, 65000, 65001, 65002, 65003, 65004, 65005, 65006, 65007, 65008, 65009, 65010, 65011, 65012, 65013, 65014, 65015, 65016, 65017, 65018, 65019, 65020, 65021, 65022, 65023, 65024, 65025, 65032, 65033, 65034, 65035, 65036, 65037, 65038, 65039, 65056, 65057, 65058, 65059, 65064, 65065, 65066, 65067, 65068, 65069, 65070, 65071, 65072, 65073, 65074, 65075, 65080, 65081, 65082, 65083, 65084, 65085, 65086, 65087, 65088, 65089, 65092, 65093, 65096, 65097, 65098, 65099, 65100, 65101, 65102, 65103, 65104, 65105, 65108, 65109, 65112, 65113, 65114, 65115, 65116, 65117, 65118, 65119, 65120, 65121, 65122, 65123, 65124, 65125, 65126, 65127, 65128, 65129, 65130, 65131, 65132, 65133, 65134, 65135, 65136, 65137, 65138, 65139, 65140, 65141, 65142, 65143, 65144, 65145, 65146, 65147, 65148, 65149, 65150, 65151, 65152, 65153, 65154, 65155, 65156, 65157, 65158, 65159, 65160, 65161, 65162, 65163, 65164, 65165, 65166, 65167, 65168, 65169, 65170, 65171, 65172, 65173, 65174, 65175, 65176, 65177, 65178, 65179, 65180, 65181, 65182, 65183, 65184, 65185, 65186, 65187, 65188, 65189, 65190, 65191, 65192, 65193, 65194, 65195, 65196, 65197, 65198, 65199, 65200, 65201, 65202, 65203, 65204, 65205, 65206, 65207, 65208, 65209, 65210, 65211, 65212, 65213, 65214, 65215, 65216, 65217, 65218, 65219, 65220, 65221, 65222, 65223, 65224, 65225, 65226, 65227, 65228, 65229, 65230, 65231, 65232, 65233, 65234, 65235, 65236, 65237, 65238, 65239, 65240, 65241, 65242, 65243, 65244, 65245, 65246, 65247, 65248, 65249, 65250, 65251, 65252, 65253, 65254, 65255, 65256, 65257, 65258, 65259, 65260, 65261, 65262, 65263, 65264, 65265, 65266, 65267, 65268, 65269, 65270, 65271, 65272, 65273, 65274, 65275, 65276, 65277, 65278, 65279, 65302, 65303, 65304, 65305, 65306, 65307, 65308, 65309, 65310, 65311, 65316, 65317, 65318, 65319, 65320, 65321, 65322, 65323, 65324, 65325, 65326, 65327, 65332, 65333, 65334, 65335, 65336, 65337, 65338, 65339, 65340, 65341, 65342, 65343, 65346, 65347, 65350, 65351, 65352, 65353, 65354, 65355, 65356, 65357, 65358, 65359, 65362, 65363, 65366, 65367, 65368, 65369, 65370, 65371, 65372, 65373, 65374, 65375, 65376, 65377, 65378, 65379, 65380, 65381, 65382, 65383, 65384, 65385, 65386, 65387, 65388, 65389, 65390, 65391, 65392, 65393, 65394, 65395, 65396, 65397, 65398, 65399, 65400, 65401, 65402, 65403, 65404, 65405, 65406, 65407, 65408, 65409, 65410, 65411, 65412, 65413, 65414, 65415, 65416, 65417, 65418, 65419, 65420, 65421, 65422, 65423, 65424, 65425, 65426, 65427, 65428, 65429, 65430, 65431, 65432, 65433, 65434, 65435, 65436, 65437, 65438, 65439, 65440, 65441, 65442, 65443, 65444, 65445, 65446, 65447, 65448, 65449, 65450, 65451, 65452, 65453, 65454, 65455, 65456, 65457, 65458, 65459, 65460, 65461, 65462, 65463, 65464, 65465, 65466, 65467, 65468, 65469, 65470, 65471, 65472, 65473, 65474, 65475, 65476, 65477, 65478, 65479, 65480, 65481, 65482, 65483, 65484, 65485, 65486, 65487, 65488, 65489, 65490, 65491, 65492, 65493, 65494, 65495, 65496, 65497, 65498, 65499, 65500, 65501, 65502, 65503, 65504, 65505, 65506, 65507, 65508, 65509, 65510, 65511, 65512, 65513, 65514, 65515, 65516, 65517, 65518, 65519, 65520, 65521, 65522, 65523, 65524, 65525, 65526, 65527, 65528, 65529, 65530, 65531, 65532, 65533, 65534, 65535
factions   TBA5

The length of the sequence for arity n is A003180(n), the number of n-ary factions.

| n |  | sequence

|
|

0  | 2  | 0, 1,
1  | 2  | 2, 3,
2  | 8  | 6, 7, 8, 9, 10, 11, 14, 15
3  | 68  | 22, 23, 24, 25, 26, 27, 30, 31, 40, 41, 42, 43, 44, 45, 46, 47, 60, 61, 62, 63, 104, 105, 106, 107, 110, 111, 126, 127, 128, 129, 130, 131, 134, 135, 136, 137, 138, 139, 142, 143, 150, 151, 152, 153, 154, 155, 158, 159, 168, 169, 170, 171, 172, 173, 174, 175, 188, 189, 190, 191, 232, 233, 234, 235, 238, 239, 254, 255,
4  | 3904  | 278, 279, 280, 281, 282, 283, 286, 287, 296, 297, 298, 299, 300, 301, 302, 303, 316, 317, 318, 319, 360, 361, 362, 363, 366, 367, 382, 383, 384, 385, 386, 387, 390, 391, 392, 393, 394, 395, 398, 399, 406, 407, 408, 409, 410, 411, 414, 415, 424, 425, 426, 427, 428, 429, 430, 431, 444, 445, 446, 447, 488, 489, 490, 491, 494, 495, 510, 511, 552, 553, 554, 555, 556, 557, 558, 559, 572, 573, 574, 575, 576, 577, 578, 579, 582, 583, 584, 585, 586, 587, 590, 591, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 616, 617, 618, 619, 620, 621, 622, 623, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 680, 681, 682, 683, 684, 685, 686, 687, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 744, 745, 746, 747, 748, 749, 750, 751, 764, 765, 766, 767, 828, 829, 830, 831, 854, 855, 856, 857, 858, 859, 862, 863, 872, 873, 874, 875, 876, 877, 878, 879, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 936, 937, 938, 939, 940, 941, 942, 943, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1020, 1021, 1022, 1023, 1632, 1633, 1634, 1635, 1638, 1639, 1640, 1641, 1642, 1643, 1646, 1647, 1650, 1651, 1654, 1655, 1656, 1657, 1658, 1659, 1662, 1663, 1664, 1665, 1666, 1667, 1670, 1671, 1672, 1673, 1674, 1675, 1678, 1679, 1680, 1681, 1682, 1683, 1686, 1687, 1688, 1689, 1690, 1691, 1694, 1695, 1696, 1697, 1698, 1699, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1760, 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34485, 34486, 34487, 34488, 34489, 34490, 34491, 34492, 34493, 34494, 34495, 34528, 34529, 34530, 34531, 34534, 34535, 34536, 34537, 34538, 34539, 34542, 34543, 34544, 34545, 34546, 34547, 34550, 34551, 34552, 34553, 34554, 34555, 34558, 34559, 34678, 34679, 34680, 34681, 34682, 34683, 34686, 34687, 34688, 34689, 34690, 34691, 34694, 34695, 34696, 34697, 34698, 34699, 34702, 34703, 34704, 34705, 34706, 34707, 34710, 34711, 34712, 34713, 34714, 34715, 34718, 34719, 34720, 34721, 34722, 34723, 34724, 34725, 34726, 34727, 34728, 34729, 34730, 34731, 34732, 34733, 34734, 34735, 34736, 34737, 34738, 34739, 34740, 34741, 34742, 34743, 34744, 34745, 34746, 34747, 34748, 34749, 34750, 34751, 34784, 34785, 34786, 34787, 34790, 34791, 34792, 34793, 34794, 34795, 34798, 34799, 34800, 34801, 34802, 34803, 34806, 34807, 34808, 34809, 34810, 34811, 34814, 34815, 34944, 34945, 34946, 34947, 34950, 34951, 34952, 34953, 34954, 34955, 34958, 34959, 34960, 34961, 34962, 34963, 34966, 34967, 34968, 34969, 34970, 34971, 34974, 34975, 34976, 34977, 34978, 34979, 34980, 34981, 34982, 34983, 34984, 34985, 34986, 34987, 34988, 34989, 34990, 34991, 34992, 34993, 34994, 34995, 34996, 34997, 34998, 34999, 35000, 35001, 35002, 35003, 35004, 35005, 35006, 35007, 35040, 35041, 35042, 35043, 35046, 35047, 35048, 35049, 35050, 35051, 35054, 35055, 35056, 35057, 35058, 35059, 35062, 35063, 35064, 35065, 35066, 35067, 35070, 35071, 35216, 35217, 35218, 35219, 35222, 35223, 35224, 35225, 35226, 35227, 35230, 35231, 35232, 35233, 35234, 35235, 35236, 35237, 35238, 35239, 35240, 35241, 35242, 35243, 35244, 35245, 35246, 35247, 35248, 35249, 35250, 35251, 35252, 35253, 35254, 35255, 35256, 35257, 35258, 35259, 35260, 35261, 35262, 35263, 35296, 35297, 35298, 35299, 35302, 35303, 35304, 35305, 35306, 35307, 35310, 35311, 35312, 35313, 35314, 35315, 35318, 35319, 35320, 35321, 35322, 35323, 35326, 35327, 35488, 35489, 35490, 35491, 35492, 35493, 35494, 35495, 35496, 35497, 35498, 35499, 35500, 35501, 35502, 35503, 35504, 35505, 35506, 35507, 35508, 35509, 35510, 35511, 35512, 35513, 35514, 35515, 35516, 35517, 35518, 35519, 35520, 35521, 35522, 35523, 35526, 35527, 35528, 35529, 35530, 35531, 35534, 35535, 35536, 35537, 35538, 35539, 35540, 35541, 35542, 35543, 35544, 35545, 35546, 35547, 35548, 35549, 35550, 35551, 35552, 35553, 35554, 35555, 35556, 35557, 35558, 35559, 35560, 35561, 35562, 35563, 35564, 35565, 35566, 35567, 35568, 35569, 35570, 35571, 35572, 35573, 35574, 35575, 35576, 35577, 35578, 35579, 35580, 35581, 35582, 35583, 35760, 35761, 35762, 35763, 35764, 35765, 35766, 35767, 35768, 35769, 35770, 35771, 35772, 35773, 35774, 35775, 35792, 35793, 35794, 35795, 35798, 35799, 35800, 35801, 35802, 35803, 35806, 35807, 35808, 35809, 35810, 35811, 35812, 35813, 35814, 35815, 35816, 35817, 35818, 35819, 35820, 35821, 35822, 35823, 35824, 35825, 35826, 35827, 35828, 35829, 35830, 35831, 35832, 35833, 35834, 35835, 35836, 35837, 35838, 35839, 36576, 36577, 36578, 36579, 36582, 36583, 36584, 36585, 36586, 36587, 36590, 36591, 36592, 36593, 36594, 36595, 36598, 36599, 36600, 36601, 36602, 36603, 36606, 36607, 36848, 36849, 36850, 36851, 36854, 36855, 36856, 36857, 36858, 36859, 36862, 36863, 38504, 38505, 38506, 38507, 38510, 38511, 38526, 38527, 38528, 38529, 38530, 38531, 38534, 38535, 38536, 38537, 38538, 38539, 38542, 38543, 38550, 38551, 38552, 38553, 38554, 38555, 38558, 38559, 38568, 38569, 38570, 38571, 38572, 38573, 38574, 38575, 38588, 38589, 38590, 38591, 38632, 38633, 38634, 38635, 38638, 38639, 38654, 38655, 38782, 38783, 38784, 38785, 38786, 38787, 38790, 38791, 38792, 38793, 38794, 38795, 38798, 38799, 38806, 38807, 38808, 38809, 38810, 38811, 38814, 38815, 38824, 38825, 38826, 38827, 38828, 38829, 38830, 38831, 38844, 38845, 38846, 38847, 38888, 38889, 38890, 38891, 38894, 38895, 38910, 38911, 39040, 39041, 39042, 39043, 39046, 39047, 39048, 39049, 39050, 39051, 39054, 39055, 39056, 39057, 39058, 39059, 39062, 39063, 39064, 39065, 39066, 39067, 39070, 39071, 39072, 39073, 39074, 39075, 39076, 39077, 39078, 39079, 39080, 39081, 39082, 39083, 39084, 39085, 39086, 39087, 39088, 39089, 39090, 39091, 39092, 39093, 39094, 39095, 39096, 39097, 39098, 39099, 39100, 39101, 39102, 39103, 39136, 39137, 39138, 39139, 39142, 39143, 39144, 39145, 39146, 39147, 39150, 39151, 39152, 39153, 39154, 39155, 39158, 39159, 39160, 39161, 39162, 39163, 39166, 39167, 39312, 39313, 39314, 39315, 39318, 39319, 39320, 39321, 39322, 39323, 39326, 39327, 39328, 39329, 39330, 39331, 39332, 39333, 39334, 39335, 39336, 39337, 39338, 39339, 39340, 39341, 39342, 39343, 39344, 39345, 39346, 39347, 39348, 39349, 39350, 39351, 39352, 39353, 39354, 39355, 39356, 39357, 39358, 39359, 39392, 39393, 39394, 39395, 39398, 39399, 39400, 39401, 39402, 39403, 39406, 39407, 39408, 39409, 39410, 39411, 39414, 39415, 39416, 39417, 39418, 39419, 39422, 39423, 39584, 39585, 39586, 39587, 39588, 39589, 39590, 39591, 39592, 39593, 39594, 39595, 39596, 39597, 39598, 39599, 39600, 39601, 39602, 39603, 39604, 39605, 39606, 39607, 39608, 39609, 39610, 39611, 39612, 39613, 39614, 39615, 39616, 39617, 39618, 39619, 39622, 39623, 39624, 39625, 39626, 39627, 39630, 39631, 39632, 39633, 39634, 39635, 39636, 39637, 39638, 39639, 39640, 39641, 39642, 39643, 39644, 39645, 39646, 39647, 39648, 39649, 39650, 39651, 39652, 39653, 39654, 39655, 39656, 39657, 39658, 39659, 39660, 39661, 39662, 39663, 39664, 39665, 39666, 39667, 39668, 39669, 39670, 39671, 39672, 39673, 39674, 39675, 39676, 39677, 39678, 39679, 39856, 39857, 39858, 39859, 39860, 39861, 39862, 39863, 39864, 39865, 39866, 39867, 39868, 39869, 39870, 39871, 39888, 39889, 39890, 39891, 39894, 39895, 39896, 39897, 39898, 39899, 39902, 39903, 39904, 39905, 39906, 39907, 39908, 39909, 39910, 39911, 39912, 39913, 39914, 39915, 39916, 39917, 39918, 39919, 39920, 39921, 39922, 39923, 39924, 39925, 39926, 39927, 39928, 39929, 39930, 39931, 39932, 39933, 39934, 39935, 40672, 40673, 40674, 40675, 40678, 40679, 40680, 40681, 40682, 40683, 40686, 40687, 40688, 40689, 40690, 40691, 40694, 40695, 40696, 40697, 40698, 40699, 40702, 40703, 40944, 40945, 40946, 40947, 40950, 40951, 40952, 40953, 40954, 40955, 40958, 40959, 43136, 43137, 43138, 43139, 43140, 43141, 43142, 43143, 43144, 43145, 43146, 43147, 43148, 43149, 43150, 43151, 43156, 43157, 43158, 43159, 43160, 43161, 43162, 43163, 43164, 43165, 43166, 43167, 43176, 43177, 43178, 43179, 43180, 43181, 43182, 43183, 43196, 43197, 43198, 43199, 43200, 43201, 43202, 43203, 43204, 43205, 43206, 43207, 43208, 43209, 43210, 43211, 43212, 43213, 43214, 43215, 43220, 43221, 43222, 43223, 43224, 43225, 43226, 43227, 43228, 43229, 43230, 43231, 43240, 43241, 43242, 43243, 43244, 43245, 43246, 43247, 43260, 43261, 43262, 43263, 43412, 43413, 43414, 43415, 43416, 43417, 43418, 43419, 43420, 43421, 43422, 43423, 43432, 43433, 43434, 43435, 43436, 43437, 43438, 43439, 43452, 43453, 43454, 43455, 43456, 43457, 43458, 43459, 43460, 43461, 43462, 43463, 43464, 43465, 43466, 43467, 43468, 43469, 43470, 43471, 43476, 43477, 43478, 43479, 43480, 43481, 43482, 43483, 43484, 43485, 43486, 43487, 43496, 43497, 43498, 43499, 43500, 43501, 43502, 43503, 43516, 43517, 43518, 43519, 43688, 43689, 43690, 43691, 43692, 43693, 43694, 43695, 43708, 43709, 43710, 43711, 43712, 43713, 43714, 43715, 43716, 43717, 43718, 43719, 43720, 43721, 43722, 43723, 43724, 43725, 43726, 43727, 43732, 43733, 43734, 43735, 43736, 43737, 43738, 43739, 43740, 43741, 43742, 43743, 43752, 43753, 43754, 43755, 43756, 43757, 43758, 43759, 43772, 43773, 43774, 43775, 43964, 43965, 43966, 43967, 43968, 43969, 43970, 43971, 43972, 43973, 43974, 43975, 43976, 43977, 43978, 43979, 43980, 43981, 43982, 43983, 43988, 43989, 43990, 43991, 43992, 43993, 43994, 43995, 43996, 43997, 43998, 43999, 44008, 44009, 44010, 44011, 44012, 44013, 44014, 44015, 44028, 44029, 44030, 44031, 44224, 44225, 44226, 44227, 44228, 44229, 44230, 44231, 44232, 44233, 44234, 44235, 44236, 44237, 44238, 44239, 44240, 44241, 44242, 44243, 44244, 44245, 44246, 44247, 44248, 44249, 44250, 44251, 44252, 44253, 44254, 44255, 44256, 44257, 44258, 44259, 44260, 44261, 44262, 44263, 44264, 44265, 44266, 44267, 44268, 44269, 44270, 44271, 44272, 44273, 44274, 44275, 44276, 44277, 44278, 44279, 44280, 44281, 44282, 44283, 44284, 44285, 44286, 44287, 44496, 44497, 44498, 44499, 44500, 44501, 44502, 44503, 44504, 44505, 44506, 44507, 44508, 44509, 44510, 44511, 44512, 44513, 44514, 44515, 44516, 44517, 44518, 44519, 44520, 44521, 44522, 44523, 44524, 44525, 44526, 44527, 44528, 44529, 44530, 44531, 44532, 44533, 44534, 44535, 44536, 44537, 44538, 44539, 44540, 44541, 44542, 44543, 44768, 44769, 44770, 44771, 44772, 44773, 44774, 44775, 44776, 44777, 44778, 44779, 44780, 44781, 44782, 44783, 44784, 44785, 44786, 44787, 44788, 44789, 44790, 44791, 44792, 44793, 44794, 44795, 44796, 44797, 44798, 44799, 45040, 45041, 45042, 45043, 45044, 45045, 45046, 45047, 45048, 45049, 45050, 45051, 45052, 45053, 45054, 45055, 48320, 48321, 48322, 48323, 48324, 48325, 48326, 48327, 48328, 48329, 48330, 48331, 48332, 48333, 48334, 48335, 48340, 48341, 48342, 48343, 48344, 48345, 48346, 48347, 48348, 48349, 48350, 48351, 48360, 48361, 48362, 48363, 48364, 48365, 48366, 48367, 48380, 48381, 48382, 48383, 48596, 48597, 48598, 48599, 48600, 48601, 48602, 48603, 48604, 48605, 48606, 48607, 48616, 48617, 48618, 48619, 48620, 48621, 48622, 48623, 48636, 48637, 48638, 48639, 48872, 48873, 48874, 48875, 48876, 48877, 48878, 48879, 48892, 48893, 48894, 48895, 49148, 49149, 49150, 49151, 59520, 59521, 59522, 59523, 59526, 59527, 59528, 59529, 59530, 59531, 59534, 59535, 59542, 59543, 59544, 59545, 59546, 59547, 59550, 59551, 59560, 59561, 59562, 59563, 59564, 59565, 59566, 59567, 59580, 59581, 59582, 59583, 59624, 59625, 59626, 59627, 59630, 59631, 59646, 59647, 59798, 59799, 59800, 59801, 59802, 59803, 59806, 59807, 59816, 59817, 59818, 59819, 59820, 59821, 59822, 59823, 59836, 59837, 59838, 59839, 59880, 59881, 59882, 59883, 59886, 59887, 59902, 59903, 60072, 60073, 60074, 60075, 60076, 60077, 60078, 60079, 60092, 60093, 60094, 60095, 60096, 60097, 60098, 60099, 60102, 60103, 60104, 60105, 60106, 60107, 60110, 60111, 60116, 60117, 60118, 60119, 60120, 60121, 60122, 60123, 60124, 60125, 60126, 60127, 60136, 60137, 60138, 60139, 60140, 60141, 60142, 60143, 60156, 60157, 60158, 60159, 60348, 60349, 60350, 60351, 60374, 60375, 60376, 60377, 60378, 60379, 60382, 60383, 60392, 60393, 60394, 60395, 60396, 60397, 60398, 60399, 60412, 60413, 60414, 60415, 61152, 61153, 61154, 61155, 61158, 61159, 61160, 61161, 61162, 61163, 61166, 61167, 61170, 61171, 61174, 61175, 61176, 61177, 61178, 61179, 61182, 61183, 61430, 61431, 61432, 61433, 61434, 61435, 61438, 61439, 65256, 65257, 65258, 65259, 65262, 65263, 65278, 65279, 65534, 65535
clans   TBA6

The length of the sequence for arity n is A000616(n), the number of n-ary clans.

| n |  | sequence

|
|

0  | 2  | 0, 1,
1  | 1  | 2,
2  | 3  | 6, 8, 9,
3  | 16  | 22, 24, 40, 41, 44, 104, 106, 107, 128, 129, 130, 131, 134, 135, 150, 151,
4  | 380  | 278, 280, 296, 300, 360, 362, 384, 386, 390, 406, 552, 553, 556, 576, 577, 584, 585, 616, 617, 640, 641, 644, 645, 660, 661, 704, 705, 708, 709, 724, 725, 1632, 1633, 1634, 1640, 1642, 1643, 1650, 1656, 1664, 1665, 1666, 1667, 1680, 1681, 1682, 1683, 1696, 1697, 1698, 1712, 1713, 1714, 2176, 2177, 2178, 2179, 2182, 2183, 2192, 2194, 2198, 2208, 2209, 2212, 2224, 2225, 2228, 2229, 2272, 2273, 2274, 2275, 2288, 2289, 2290, 2448, 2449, 2450, 2451, 2454, 2455, 2480, 2481, 2484, 2528, 2529, 2530, 5736, 5737, 5760, 5761, 5762, 5763, 5768, 5769, 5770, 5771, 6272, 6273, 6274, 6275, 6278, 6279, 6280, 6281, 6282, 6283, 6286, 6287, 6304, 6305, 6306, 6307, 6308, 6310, 6312, 6313, 6316, 6317, 6368, 6369, 6370, 6371, 6376, 6377, 6378, 6382, 6383, 10368, 10369, 10372, 10373, 10376, 10377, 10378, 10379, 10380, 10382, 10388, 10389, 10396, 10397, 10398, 10399, 10432, 10433, 10434, 10435, 10436, 10437, 10440, 10441, 10442, 10443, 10444, 10445, 10446, 10447, 10644, 10645, 10652, 10654, 10688, 10689, 10690, 10691, 10692, 10693, 10696, 10698, 10700, 10701, 10702, 10703, 26752, 26753, 26754, 26755, 26758, 26759, 26760, 26761, 26762, 26763, 26766, 26767, 26776, 26777, 26778, 26782, 26783, 27304, 27306, 27307, 27308, 27309, 27324, 27580, 27581, 32768, 32769, 32770, 32771, 32774, 32775, 32776, 32777, 32778, 32779, 32782, 32783, 32790, 32791, 32792, 32793, 32794, 32795, 32798, 32799, 32808, 32809, 32810, 32811, 32812, 32813, 32814, 32815, 32828, 32829, 32830, 32831, 32872, 32873, 32874, 32875, 32878, 32879, 32894, 32895, 33046, 33047, 33048, 33049, 33050, 33051, 33054, 33055, 33064, 33065, 33066, 33067, 33068, 33069, 33070, 33071, 33084, 33085, 33086, 33087, 33128, 33129, 33130, 33131, 33134, 33135, 33150, 33151, 33320, 33321, 33322, 33323, 33324, 33325, 33326, 33327, 33340, 33341, 33342, 33343, 33344, 33345, 33346, 33347, 33350, 33351, 33352, 33353, 33354, 33355, 33358, 33359, 33364, 33365, 33366, 33367, 33368, 33369, 33370, 33371, 33372, 33373, 33374, 33375, 33384, 33385, 33386, 33387, 33388, 33389, 33390, 33391, 33404, 33405, 33406, 33407, 33596, 33597, 33598, 33599, 33622, 33623, 33624, 33625, 33626, 33627, 33630, 33631, 33640, 33641, 33642, 33643, 33644, 33645, 33646, 33647, 33660, 33661, 33662, 33663, 34400, 34401, 34402, 34403, 34406, 34407, 34408, 34409, 34410, 34411, 34414, 34415, 34418, 34419, 34422, 34423, 34424, 34425, 34426, 34427, 34430, 34431, 34678, 34679, 34680, 34681, 34682, 34683, 34686, 34687, 38504, 38505, 38506, 38507, 38510, 38511, 38526, 38527, 38782, 38783

### self-complementary

[edit | edit source]

Balanced families and clans can contain their own complements.

The sequence for clans is a subsequence of the one for families. All entries are even.

families   TBA2

The length of the sequence for arity n is A001320(n), the number of self-complementary n-ary families.

| n |  | sequence

|
|

1  | 1  | 2,
2  | 2  | 4, 6,
3  | 11  | 16, 18, 20, 22, 24, 36, 44, 66, 74, 98, 104,
4  | 226  | 256, 258, 260, 262, 264, 272, 274, 276, 278, 280, 288, 292, 296, 300, 320, 322, 328, 330, 352, 354, 360, 362, 384, 386, 388, 390, 400, 402, 404, 406, 516, 524, 528, 532, 536, 540, 548, 556, 560, 564, 568, 572, 1026, 1034, 1040, 1042, 1048, 1050, 1090, 1098, 1104, 1106, 1112, 1114, 1538, 1544, 1552, 1554, 1560, 1562, 1634, 1640, 1648, 1650, 1656, 1658, 2064, 2066, 2068, 2070, 2192, 2194, 2196, 2198, 2320, 2322, 2324, 2326, 2432, 2434, 2436, 2438, 4098, 4100, 4102, 4130, 4132, 4134, 4162, 4164, 4166, 4194, 4196, 4198, 4610, 4612, 4614, 4640, 4644, 4646, 4682, 4684, 4686, 4712, 4716, 4718, 5122, 5124, 5126, 5162, 5164, 5166, 5184, 5186, 5190, 5224, 5226, 5230, 5634, 5636, 5638, 5672, 5676, 5678, 5704, 5706, 5710, 5728, 5730, 5732, 8196, 8198, 8212, 8214, 8324, 8326, 8340, 8342, 8452, 8454, 8468, 8470, 8576, 8578, 8592, 8594, 10244, 10246, 10256, 10258, 10380, 10382, 10392, 10394, 10500, 10502, 10512, 10514, 10632, 10634, 10652, 10654, 16386, 16390, 16402, 16406, 16514, 16518, 16530, 16534, 16642, 16646, 16658, 16662, 16768, 16772, 16784, 16788, 18434, 18438, 18448, 18452, 18570, 18574, 18584, 18588, 18690, 18694, 18704, 18708, 18824, 18828, 18842, 18846, 24578, 24580, 24594, 24596, 24738, 24740, 24754, 24756, 24834, 24836, 24850, 24852, 24992, 24998, 25008, 25014, 27138, 27140, 27152, 27158, 27304, 27310, 27322, 27324, 27394, 27396, 27408, 27414, 27562, 27564, 27576, 27582
clans   TBA3

The length of the sequence for arity n is A000610(n), the number of self-complementary n-ary clans.

| n |  | sequence

|
|

1  | 1  | 2,
2  | 1  | 6,
3  | 4  | 22, 24, 44, 104,
4  | 36  | 278, 280, 296, 300, 360, 362, 384, 386, 390, 406, 556, 1634, 1640, 1650, 1656, 1698, 1714, 2192, 2194, 2198, 2212, 2290, 2484, 2530, 6308, 6310, 6378, 10380, 10382, 10652, 10654, 10696, 10698, 26778, 27304, 27324

## misc.

[edit | edit source]

A211344 T ( n , n − k ) {\displaystyle T(n,n-k)} is the  n {\displaystyle n} -ary truth table of  x k {\displaystyle x_{k}}

A227724 T ( n , k ) {\displaystyle T(n,k)} is the number of balanced n-ary families of size  2 k {\displaystyle 2^{k}}
A227725 T ( n , k ) {\displaystyle T(n,k)} is the number of  n {\displaystyle n} -ary families of size  2 k {\displaystyle 2^{k}}
A051502 a ( n ) {\displaystyle a(n)} is the number of  n {\displaystyle n} -ary families of maximal size  2 n {\displaystyle 2^{n}}

A000371 a ( n ) {\displaystyle a(n)} is the number of truly  n {\displaystyle n} -ary functions   (number of nondegenerate Boolean functions of  n {\displaystyle n} variables)

Monotonic: A000372 (Dedekind numbers) counts functions, A003182 counts clans (which are probably the same as factions)

|  | 0 | 1 | 2 | 3 | 4

|
|
|
|
|
|

male | A246418 | 1 | 3 | 13 | 159 | 33337
female | A246537 | 1 | 1 | 3 | 97 | 32199

Google food

| number of super-families  | 1, 2, 5, 30, 2288, 67172352

|

number of super-clans  | 1, 2, 4, 14, 222, 616126
number of new blightless clans  | 2, 0, 1, 11, 343
number of blightless clans  | 2, 2, 3, 14, 357
number of new blighted clans  | 0, 1, 2, 5, 37
number of blighted clans  | 0, 1, 3, 8, 45
TBA1 | 1, 3, 14, 870, 18796230
TBA2 | 2, 4, 6, 16, 18, 20, 22, 24, 36, 44, 66, 74, 98, 104, 256, 258, 260, 262, 264, 272, 274, 276, 278, 280, 288, 292, 296, 300
TBA2 / 2  | 1, 2, 3, 8, 9, 10, 11, 12, 18, 22, 33, 37, 49, 52, 128, 129, 130, 131, 132, 136, 137, 138, 139, 140, 144, 146, 148, 150
TBA3 | 2, 6, 22, 24, 44, 104, 278, 280, 296, 300
TBA3 / 2  | 1, 3, 11, 12, 22, 52, 139, 140, 148, 150
TBA4 | 0, 1, 2, 4, 6, 8, 9, 16, 18, 20, 22, 24, 32, 33, 36, 40, 41, 44, 64, 65, 66, 72, 73, 74, 96, 97, 98, 104, 106, 107, 128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146
TBA5 | 0, 1, 2, 3, 6, 7, 8, 9, 10, 11, 14, 15, 22, 23, 24, 25, 26, 27, 30, 31, 40, 41, 42, 43, 44, 45, 46, 47, 60, 61, 62, 63, 104, 105, 106, 107, 110, 111, 126, 127, 128, 129
TBA6 | 0, 1, 2, 6, 8, 9, 22, 24, 40, 41, 44, 104, 106, 107, 128, 129, 130, 131, 134, 135, 150, 151, 278, 280, 296, 300, 360, 362, 384, 386, 390, 406, 552, 553, 556, 576, 577, 584
TBA7 | 2, 4, 14, 184, 51564
TBA7 / 2  | 1, 2, 7, 92, 25782
TBA8 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 50