Triangle Orange

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 Orange

Birch with columns multiplied by Agave

🌊    triangle Orange    row sums Chamomile
k
n
 0 1 2 3 4 5 sums
0 1 · 0 0 0
1 0 · 0 0 1 · 1 1 1
2 0 · 0 0 1 · 1 1 1 · 0 0 1
3 0 · 0 0 1 · 1 1 4 · 0 0 1 · 7 7 8
4 0 · 0 0 1 · 1 1 13 · 0 0 11 · 7 77 1 · 750 750 828
5 0 · 0 0 1 · 1 1 40 · 0 0 90 · 7 630 26 · 750 19500 1 · 18771864 18771864 18791995
(a, s) ↦ balanced dense families Orange(a, s) is the number of balanced dense families with arity a and strength s.

Triangle ExOrange

Birch with columns multiplied by ExAgave

🌊    triangle ExOrange    row sums Calendula (A378302)
k
n
 0 1 2 3 4 5 sums
0 1 · 0 0 0
1 0 · 0 0 1 · 2 2 2
2 0 · 0 0 1 · 2 2 1 · 0 0 2
3 0 · 0 0 1 · 2 2 4 · 0 0 1 · 56 56 58
4 0 · 0 0 1 · 2 2 13 · 0 0 11 · 56 616 1 · 12000 12000 12618
5 0 · 0 0 1 · 2 2 40 · 0 0 90 · 56 5040 26 · 12000 312000 1 · 600699648 600699648 601016690
(a, s) ↦ balanced dense BF ExOrange(a, s) is the number of balanced dense BF with arity a and strength s.
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