Sequence Dandelion

Studies of Boolean functions
sequences related to Boolean functions

Sequences Dandelion_(Drop)

${\text{Dandelion}}(n)={\color {Red}2^{2^{n}-n-1}}\cdot ({\color {Green}2^{2^{n}}-1})$ Dandelion = Sage · SmallGrass

row sums of Forsythia_(Drop)

Oak with columns multiplied by truncated Aloe

🌊 triangle Forsythia row sums Dandelion
k n	0	1	2	3	4	5	sums
0	1 · 1 1						1
1	1 · 1 1	1 · 2 2					3
2	1 · 1 1	3 · 2 6	1 · 23 23				30
3	1 · 1 1	7 · 2 14	7 · 23 161	1 · 3904 3904			4080
4	1 · 1 1	15 · 2 30	35 · 23 805	15 · 3904 58560	1 · 134156284 134156284		134215680
5	1 · 1 1	31 · 2 62	155 · 23 3565	155 · 3904 605120	31 · 134156284 4158844804	1 · 288230371925149328 288230371925149328	288230376084602880

OakDrop with columns multiplied by truncated Aloe

💧 triangle ForsythiaDrop row sums DandelionDrop
k n	0	1	2	3	4	5	sums
0	1 · 1 1						1
1	0	1 · 2 2					2
2	0	2 · 2 4	1 · 23 23				27
3	0	4 · 2 8	6 · 23 138	1 · 3904 3904			4050
4	0	8 · 2 16	28 · 23 644	14 · 3904 54656	1 · 134156284 134156284		134211600
5	0	16 · 2 32	120 · 23 2760	140 · 3904 546560	30 · 134156284 4024688520	1 · 288230371925149328 288230371925149328	288230375950387200