Triangle Laurel

Studies of Boolean functions
sequences related to Boolean functions

triangles by arity and strength
	base triangle	diagonal	families		BF
	base triangle	diagonal	triangle	total	triangle	total
all	Oak	(Ex)Aloe	Olive	Thyme	ExOlive	Grass
balanced	Oak	(Ex)Agave	Laurel	Saffron	ExLaurel	Sesame
dense	Birch	(Ex)Aloe	Lemon	Lily	ExLemon	Lotus
b & d	Birch	(Ex)Agave	Orange	Chamomile	ExOrange	Calendula

Triangle Oak with multiplied columns

Triangles Laurel_(Drop)

The diagonal of both triangles is Agave.

Oak with columns multiplied by Agave

🌊 triangle Laurel (A227724) row sums Saffron
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	3 · 1 3	1 · 0 0				3
3	1 · 0 0	7 · 1 7	7 · 0 0	1 · 7 7			14
4	1 · 0 0	15 · 1 15	35 · 0 0	15 · 7 105	1 · 750 750		870
5	1 · 0 0	31 · 1 31	155 · 0 0	155 · 7 1085	31 · 750 23250	1 · 18771864 18771864	18796230

OakDrop with columns multiplied by Agave

💧 triangle LaurelDrop row sums SaffronDrop
k n	0	1	2	3	4	5	sums
0	1 · 0 0						0
1	0	1 · 1 1					1
2	0	2 · 1 2	1 · 0 0				2
3	0	4 · 1 4	6 · 0 0	1 · 7 7			11
4	0	8 · 1 8	28 · 0 0	14 · 7 98	1 · 750 750		856
5	0	16 · 1 16	120 · 0 0	140 · 7 980	30 · 750 22500	1 · 18771864 18771864	18795360

(a, s) ↦ balanced families

Olive(a, s)
OliveDrop(a, s)

is the number of balanced families with

a and strength s.

The diagonal of both triangles is ExAgave.

Oak with columns multiplied by ExAgave

🌊 triangle ExLaurel row sums Sesame (~A037293)
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	3 · 2 6	1 · 0 0				6
3	1 · 0 0	7 · 2 14	7 · 0 0	1 · 56 56			70
4	1 · 0 0	15 · 2 30	35 · 0 0	15 · 56 840	1 · 12000 12000		12870
5	1 · 0 0	31 · 2 62	155 · 0 0	155 · 56 8680	31 · 12000 372000	1 · 600699648 600699648	601080390

OakDrop with columns multiplied by ExAgave

💧 triangle ExLaurelDrop row sums SesameDrop
k n	0	1	2	3	4	5	sums
0	1 · 0 0						0
1	0	1 · 2 2					2
2	0	2 · 2 4	1 · 0 0				4
3	0	4 · 2 8	6 · 0 0	1 · 56 56			64
4	0	8 · 2 16	28 · 0 0	14 · 56 784	1 · 12000 12000		12800
5	0	16 · 2 32	120 · 0 0	140 · 56 7840	30 · 12000 360000	1 · 600699648 600699648	601067520

(a, s) ↦ balanced BF

ExLaurel(a, s)
ExLaurelDrop(a, s)

is the number of balanced BF with

a and strength s.