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
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 (~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
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
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