Sequence Saffron

Studies of Boolean functions
sequences related to Boolean functions

triangles by arity and strength  | base
triangle  | diagonal  | families | BF

|
|
|
|

triangle  | total  | triangle  | total
all  | Oak | (Ex)Aloe | Olive | Thyme | ExOlive | Grass
balanced | (Ex)Agave | Laurel | Saffron | ExLaurel | Sesame
dense | Birch | (Ex)Aloe | Lemon | Lily | ExLemon | Lotus
b & d | (Ex)Agave | Orange | Chamomile | ExOrange | Calendula

## Sequences Saffron(Drop)

[edit | edit source]

| 0 | 1 | 2 | 3 | 4 | 5

|
|
|
|
|
|

🌊 Saffron | 0 | 1 | 3 | 14 | 870 | 18796230
💧 SaffronDrop | 0 | 1 | 2 | 11 | 856 | 18795360

Saffron is the central column of tiara Emerald.

a ↦ balanced families  | Saffron(a)
SaffronDrop(a) | is the number of balanced families with  | arity
adicity | a.

|
|
|
|

row sums of Laurel(Drop)

Oak with columns multiplied by Agave

| 🌊    triangle Laurel (A227724)    row sums Saffron

| 0 | 1 | 2 | 3 | 4 | 5 | sums
0  | 1 · 0 0  |  |  |  |  |  | 0
1  | 1 · 0 0  | 1 · 1 1  |  |  |  |  | 1
2  | 1 · 0 0  | 3 · 1 3  | 1 · 0 0  |  |  |  | 3
3  | 1 · 0 0  | 7 · 1 7  | 7 · 0 0  | 1 · 7 7  |  |  | 14
4  | 1 · 0 0  | 15 · 1 15  | 35 · 0 0  | 15 · 7 105  | 1 · 750 750  |  | 870
5  | 1 · 0 0  | 31 · 1 31  | 155 · 0 0  | 155 · 7 1085  | 31 · 750 23250  | 1 · 18771864 18771864  | 18796230

OakDrop with columns multiplied by Agave

| 💧    triangle LaurelDrop    row sums SaffronDrop

| 0 | 1 | 2 | 3 | 4 | 5 | sums
0  | 1 · 0 0  |  |  |  |  |  | 0
1  |   0  | 1 · 1 1  |  |  |  |  | 1
2  |   0  | 2 · 1 2  | 1 · 0 0  |  |  |  | 2
3  |   0  | 4 · 1 4  | 6 · 0 0  | 1 · 7 7  |  |  | 11
4  |   0  | 8 · 1 8  | 28 · 0 0  | 14 · 7 98  | 1 · 750 750  |  | 856
5  |   0  | 16 · 1 16  | 120 · 0 0  | 140 · 7 980  | 30 · 750 22500  | 1 · 18771864 18771864  | 18795360

14,
870,
18796230,
28634752793916486,
187118328452563149209991044344449606,
22533823529098462258163079522899558179092788838542277982316450977506091590,
922955670224540869119149160256223416949630303989222426908845428034308731131863057623892273579722854259228632672010201445381801768215665533633663386182,
4376225148534151181664223486798176933608699081120836908609460839262474322862734028116293105539955137056806087908807229299812013351930172713574095687135839340332815801390464700679415721755397234951104278389752312048646948376664461972339533387772739208990822848401012423551863454109614426370669961581838918

*[BF]: Boolean functions
*[b & d]: balanced and dense