Sequence Sesame

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 Sesame_(Drop)

	0	1	2	3	4	5	6	7
🌊 Sesame ~A037293	0	2	6	70	12870	601080390	1832624140942590534	23951146041928082866135587776380551750
💧 SesameDrop	0	2	4	64	12800	601067520	1832624140341510144	23951146041928082864302963635437961216

a ↦ balanced BF

Sesame(a) SesameDrop(a)

is the number of balanced BF with

arity adicity

a.

Sesame is the diagonal of Oleander. Through SignedOleander it is part of the definition of Calendula, the number of balanced dense BF.

row sums of ExLaurel(Drop)

Oak with columns multiplied by ExAgave 🌊    triangle ExLaurel    row sums Sesame (~A037293) k n 0 1 2 3 4 5 sums 0 1 · 0 0 0 1 1 · 0 0 1 · 2 2 2 2 1 · 0 0 3 · 2 6 1 · 0 0 6 3 1 · 0 0 7 · 2 14 7 · 0 0 1 · 56 56 70 4 1 · 0 0 15 · 2 30 35 · 0 0 15 · 56 840 1 · 12000 12000 12870 5 1 · 0 0 31 · 2 62 155 · 0 0 155 · 56 8680 31 · 12000 372000 1 · 600699648 600699648 601080390 OakDrop with columns multiplied by ExAgave 💧    triangle ExLaurelDrop    row sums SesameDrop k n 0 1 2 3 4 5 sums 0 1 · 0 0 0 1   0 1 · 2 2 2 2   0 2 · 2 4 1 · 0 0 4 3   0 4 · 2 8 6 · 0 0 1 · 56 56 64 4   0 8 · 2 16 28 · 0 0 14 · 56 784 1 · 12000 12000 12800 5   0 16 · 2 32 120 · 0 0 140 · 56 7840 30 · 12000 360000 1 · 600699648 600699648 601067520