Sequences related to strong Boolean functions

Studies of Boolean functions
sequences related to Boolean functions

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

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triangle  | total  | triangle  | total
balanced | Oak | (Ex)Agave | Laurel | Saffron | ExLaurel | Sesame
all  | (Ex)Aloe | Olive | Thyme | ExOlive | Grass
dense | Birch | Lemon | Lily | ExLemon | Lotus

## Sequence Aloe

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| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7

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Aloe (A051502) | 2 | 1 | 2 | 23 | 3904 | 134156284 | 288230371925149328 | 2658455991569831727504985413859223552
ExAloe | 2 | 2 | 8 | 184 | 62464 | 4293001088 | 18446743803209556992 | 340282366920938461120638132973980614656
a ↦ strong families  | Aloe(a) is the number of strong families with arity a.

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Aloe ∘ powers of two = ExAloe

Oak ∘ (Ex)Aloe = (Ex)Olive

Oak ∘ truncated Aloe = Forsythia

Aloe can indirectly be defined with triangle SignedCypress, which is based on Oak, and whose row sums are SmallExAloe.

## Sequence Agave

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| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7

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NonAgave | 2 | 0 | 2 | 16 | 3154 | 115384420 | 259595620314358352 | 2471337663117268581931607874158730240
Agave | 0 | 1 | 0 | 7 | 750 | 18771864 | 28634751610790976 | 187118328452563145573377539700493312
ExAgave | 0 | 2 | 0 | 56 | 12000 | 600699648 | 1832624103090622464 | 23951146041928082633392325081663143936
a ↦ strong balanced families  | Agave(a) is the number of strong balanced families with arity a.

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Agave ∘ powers of two = ExAgave

NonAgave = Aloe − Agave That is the number of balanced families, that are not strong.

Oak ∘ (Ex)Agave = (Ex)Laurel
*[BF]: number of Boolean functions