Triangle Olearia

Studies of Boolean functions
sequences related to Boolean functions

Triangles Olearia(Drop)

The unsigned triangles are shown for the sake of completeness, and do not seem to be interesting.

Pascal with columns multiplied by Saffron

🌊    triangle Olearia
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 2 · 1 2 1 · 3 3 5
3 1 · 0 0 3 · 1 3 3 · 3 9 1 · 14 14 26
4 1 · 0 0 4 · 1 4 6 · 3 18 4 · 14 56 1 · 870 870 948
5 1 · 0 0 5 · 1 5 10 · 3 30 10 · 14 140 5 · 870 4350 1 · 18796230 18796230 18800755

PascalDrop with columns multiplied by Saffron

💧    triangle OleariaDrop
k
n
 0 1 2 3 4 5 sums
0 1 · 0 0 0
1   0 1 · 1 1 1
2   0 1 · 1 1 1 · 3 3 4
3   0 1 · 1 1 2 · 3 6 1 · 14 14 21
4   0 1 · 1 1 3 · 3 9 3 · 14 42 1 · 870 870 922
5   0 1 · 1 1 4 · 3 12 6 · 14 84 4 · 870 3480 1 · 18796230 18796230 18799807

Triangle SignedOlearia

signed triangles
base
triangle 		families BF
diagonal triangle total diagonal triangle total
strong Turned
Rhodo. 		Thyme SignedBerberis Aloe Grass SignedBramble ExAloe
balanced & strong Saffron SignedArdisia Agave Sesame SignedAronia ExAgave
dense Pascal Thyme SignedCypress Lily Grass SignedCedar Lotus
balanced & dense Saffron SignedOlearia Chamomile Sesame SignedOleander Calendula

The absolute values are Pascal with columns multiplied by Saffron.

triangle SignedOlearia    row sums Chamomile
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 2 · 1 −2 1 · 3 3 1
3 1 · 0 0 3 · 1 3 3 · 3 −9 1 · 14 14 8
4 1 · 0 0 4 · 1 −4 6 · 3 18 4 · 14 −56 1 · 870 870 828
5 1 · 0 0 5 · 1 5 10 · 3 −30 10 · 14 140 5 · 870 −4350 1 · 18796230 18796230 18791995
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