Triangle Laurel

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
Triangle Oak with multiplied columns

Triangles Laurel(Drop)

The diagonal of both triangles is Agave.

Oak with columns multiplied by Agave

🌊    triangle Laurel (A227724)    row sums Saffron
k
n
 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
k
n
 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
(a, s) ↦ balanced families Olive(a, s)
OliveDrop(a, s) 		is the number of balanced families with arity
adicity 		a and strength s.

Triangles ExLaurel(Drop)

The diagonal of both triangles is ExAgave.

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
(a, s) ↦ balanced BF ExLaurel(a, s)
ExLaurelDrop(a, s) 		is the number of balanced BF with arity
adicity 		a and strength s.
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