Sequence Crocus

Studies of Boolean functions
sequences related to Boolean functions
gender
diagonal triangle total
♀ Violet Robinia Primula
♂ HalfGrass HalfCedar HalfCrocus
all Lotus Willow Grass
♂ − ♀ NonLotus Hickory Hyacinth

Crocus = Hyacinth + Grass
HalfCrocus = Hyacinth + Primula

Sequences Crocus(Drop)

0 1 2 3 4 5 6 7
🌊 Crocus (2·A246418) 2 6 26 318 66674 4295297718 18446744099480343818 340282366920938463592501816037931689070
💧 CrocusDrop 2 4 20 292 66356 4295231044 18446744095185046100 340282366920938463574055071938451345252

half
0 1 2 3 4 5 6 7
🌊 HalfCrocus (A246418) 1 3 13 159 33337 2147648859 9223372049740171909 170141183460469231796250908018965844535
💧 HalfCrocusDrop 1 2 10 146 33178 2147615522 9223372047592523050 170141183460469231787027535969225672626
a ↦ ♂ HalfCrocus(a)
HalfCrocusDrop(a) 		is the number of male BF with arity
adicity 		a.
row sums of Cedar(Drop)

Pascal with columns multiplied by Grass

🌊    triangle Cedar    row sums Crocus
k
n
 0 1 2 3 4 5 sums
0 1 · 2 2 2
1 1 · 2 2 1 · 4 4 6
2 1 · 2 2 2 · 4 8 1 · 16 16 26
3 1 · 2 2 3 · 4 12 3 · 16 48 1 · 256 256 318
4 1 · 2 2 4 · 4 16 6 · 16 96 4 · 256 1024 1 · 65536 65536 66674
5 1 · 2 2 5 · 4 20 10 · 16 160 10 · 256 2560 5 · 65536 327680 1 · 4294967296 4294967296 4295297718

PascalDrop with columns multiplied by Grass

💧    triangle CedarDrop    row sums CrocusDrop
k
n
 0 1 2 3 4 5 sums
0 1 · 2 2 2
1   0 1 · 4 4 4
2   0 1 · 4 4 1 · 16 16 20
3   0 1 · 4 4 2 · 16 32 1 · 256 256 292
4   0 1 · 4 4 3 · 16 48 3 · 256 768 1 · 65536 65536 66356
5   0 1 · 4 4 4 · 16 64 6 · 256 1536 4 · 65536 262144 1 · 4294967296 4294967296 4295231044
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