Triangles Chestnut and Chinkapin

Studies of Boolean functions
sequences related to Boolean functions
Pascal's triangle with multiplied columns

Triangles Chestnut(Drop)

Pascal with columns multiplied by Pansy

🌊    triangle Chestnut    row sums ~Grass
k
n
 0 1 2 3 4 5 sums
0 1 · 2 2 2
1 1 · 2 2 1 · 0 0 2
2 1 · 2 2 2 · 0 0 1 · 2 2 4
3 1 · 2 2 3 · 0 0 3 · 2 6 1 · 8 8 16
4 1 · 2 2 4 · 0 0 6 · 2 12 4 · 8 32 1 · 210 210 256
5 1 · 2 2 5 · 0 0 10 · 2 20 10 · 8 80 5 · 210 1050 1 · 64384 64384 65536

PascalDrop with columns multiplied by Pansy

💧    triangle ChestnutDrop    row sums ~GrassDrop
k
n
 0 1 2 3 4 5 sums
0 1 · 2 2 2
1   0 1 · 0 0 0
2   0 1 · 0 0 1 · 2 2 2
3   0 1 · 0 0 2 · 2 4 1 · 8 8 12
4   0 1 · 0 0 3 · 2 6 3 · 8 24 1 · 210 210 240
5   0 1 · 0 0 4 · 2 8 6 · 8 48 4 · 210 840 1 · 64384 64384 65280
(a, v) ↦ self-reverse Chestnut(a, v)
ChestnutDrop(a, v) 		is the number of self-reverse BF with arity
adicity 		a and valency v.

Triangles Chinkapin(Drop)

Pascal with columns multiplied by Peony

🌊    triangle Chinkapin    row sums ~Grass
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 2 · 2 4 1 · 0 0 4
3 1 · 0 0 3 · 2 6 3 · 0 0 1 · 10 10 16
4 1 · 0 0 4 · 2 8 6 · 0 0 4 · 10 40 1 · 208 208 256
5 1 · 0 0 5 · 2 10 10 · 0 0 10 · 10 100 5 · 208 1040 1 · 64386 64386 65536

PascalDrop with columns multiplied by Peony

💧    triangle ChinkapinDrop    row sums ~GrassDrop
k
n
 0 1 2 3 4 5 sums
0 1 · 0 0 0
1   0 1 · 2 2 2
2   0 1 · 2 2 1 · 0 0 2
3   0 1 · 2 2 2 · 0 0 1 · 10 10 12
4   0 1 · 2 2 3 · 0 0 3 · 10 30 1 · 208 208 240
5   0 1 · 2 2 4 · 0 0 6 · 10 60 4 · 208 832 1 · 64386 64386 65280
(a, v) ↦ self-dual Chinkapin(a, v)
ChinkapinDrop(a, v) 		is the number of self-dual BF with arity
adicity 		a and valency v.
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