Triangle Olive

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 Olive(Drop)

The diagonal of both triangles is Aloe.

Oak with columns multiplied by Aloe

🌊    triangle Olive (A227725)    row sums Thyme (A000231)
k
n
 0 1 2 3 4 5 sums
0 1 · 2 2 2
1 1 · 2 2 1 · 1 1 3
2 1 · 2 2 3 · 1 3 1 · 2 2 7
3 1 · 2 2 7 · 1 7 7 · 2 14 1 · 23 23 46
4 1 · 2 2 15 · 1 15 35 · 2 70 15 · 23 345 1 · 3904 3904 4336
5 1 · 2 2 31 · 1 31 155 · 2 310 155 · 23 3565 31 · 3904 121024 1 · 134156284 134156284 134281216

OakDrop with columns multiplied by Aloe

💧    triangle OliveDrop    row sums ThymeDrop
k
n
 0 1 2 3 4 5 sums
0 1 · 2 2 2
1   0 1 · 1 1 1
2   0 2 · 1 2 1 · 2 2 4
3   0 4 · 1 4 6 · 2 12 1 · 23 23 39
4   0 8 · 1 8 28 · 2 56 14 · 23 322 1 · 3904 3904 4290
5   0 16 · 1 16 120 · 2 240 140 · 23 3220 30 · 3904 117120 1 · 134156284 134156284 134276880
(a, s) ↦ families Olive(a, s)
OliveDrop(a, s) 		is the number of families with arity
adicity 		a and strength s.
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