Sequence Sesame

Studies of Boolean functions
sequences related to Boolean functions

triangles by arity and strength
	base triangle	diagonal	families		BF
	base triangle	diagonal	triangle	total	triangle	total
all	Oak	(Ex)Aloe	Olive	Thyme	ExOlive	Grass
balanced	Oak	(Ex)Agave	Laurel	Saffron	ExLaurel	Sesame
dense	Birch	(Ex)Aloe	Lemon	Lily	ExLemon	Lotus
b & d	Birch	(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

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