Sequence Heather

Clover is the summation of Heather, which is the summation of Lavender. Compare triangle Lime.

Sequences Clover and Heather

	0	1	2	3	4	5	6	7
🌊 Clover (A076766)	1	2	4	8	16	32	68	148
💧 Heather (~A034343)	1	1	2	4	8	16	36	80

Compare MaimedClover. The differences of Clover and the powers of two are A250003.

row sums of Elm and Lime

🌊 triangle Elm (A076831) row sums Clover (A076766)
k n	0	1	2	3	4	5	6	7	sums
0	1								1
1	1	1							2
2	1	2	1						4
3	1	3	3	1					8
4	1	4	6	4	1				16
5	1	5	10	10	5	1			32
6	1	6	16	22	16	6	1		68
7	1	7	23	43	43	23	7	1	148

💧 triangle Lime (~A034253) row sums Heather (~A034343)
k n	0	1	2	3	4	5	6	7	sums
0	1								1
1	0	1							1
2	0	1	1						2
3	0	1	2	1					4
4	0	1	3	3	1				8
5	0	1	4	6	4	1			16
6	0	1	6	12	11	5	1		36
7	0	1	7	21	27	17	6	1	80

row sums of StackedHeather and DiagonalHeather

🌊 triangle StackedHeather row sums Clover
k n	0	1	2	3	4	5	6	7	sums
0	1								1
1	1	1							2
2	1	1	2						4
3	1	1	2	4					8
4	1	1	2	4	8				16
5	1	1	2	4	8	16			32
6	1	1	2	4	8	16	36		68
7	1	1	2	4	8	16	36	80	148

💧 triangle DiagonalHeather row sums Heather
k n	0	1	2	3	4	5	6	7	sums
0	1								1
1	0	1							1
2	0	0	2						2
3	0	0	0	4					4
4	0	0	0	0	8				8
5	0	0	0	0	0	16			16
6	0	0	0	0	0	0	36		36
7	0	0	0	0	0	0	0	80	80

row sums of SlopedHeather and SlopedLavender

🌊 triangle SlopedHeather row sums Clover
k n	0	1	2	3	4	5	6	7	sums
0	1								1
1	1	1							2
2	2	1	1						4
3	4	2	1	1					8
4	8	4	2	1	1				16
5	16	8	4	2	1	1			32
6	36	16	8	4	2	1	1		68
7	80	36	16	8	4	2	1	1	148

💧 triangle SlopedLavender row sums Heather
k n	0	1	2	3	4	5	6	7	sums
0	1								1
1	0	1							1
2	1	0	1						2
3	2	1	0	1					4
4	4	2	1	0	1				8
5	8	4	2	1	0	1			16
6	20	8	4	2	1	0	1		36
7	44	20	8	4	2	1	0	1	80

a ↦ houses

Clover(a)
Heather(a)

is the number of houses of the seals with

a.

	0	1	2	3	4	5	6	7
🌊 Heather (~A034343)	1	1	2	4	8	16	36	80
💧 Lavender	1	0	1	2	4	8	20	44

row sums of TurnedLime and Magnolia

🌊 triangle TurnedLime (~A034253) row sums Heather (~A034343)
k n	0	1	2	3	4	5	6	7	8	9	10	11	12	sums
0	1													1
1	1	0												1
2	1	1	0											2
3	1	2	1	0										4
4	1	3	3	1	0									8
5	1	4	6	4	1	0								16
6	1	5	11	12	6	1	0							36
7	1	6	17	27	21	7	1	0						80
8	1	7	25	54	63	34	9	1	0					194
9	1	8	35	99	163	134	54	11	1	0				506
10	1	9	47	170	385	465	276	82	13	1	0			1449
11	1	10	61	277	847	1472	1283	544	120	15	1	0		4631
12	1	11	78	436	1775	4408	5676	3480	1048	174	18	1	0	17106

💧 triangle Magnolia row sums Lavender
k n	0	1	2	3	4	5	6	7	8	9	10	11	12	sums
0	1													1
1	0	0												0
2	0	1	0											1
3	0	1	1	0										2
4	0	1	2	1	0									4
5	0	1	3	3	1	0								8
6	0	1	5	8	5	1	0							20
7	0	1	6	15	15	6	1	0						44
8	0	1	8	27	42	27	8	1	0					114
9	0	1	10	45	100	100	45	10	1	0				312
10	0	1	12	71	222	331	222	71	12	1	0			943
11	0	1	14	107	462	1007	1007	462	107	14	1	0		3182
12	0	1	17	159	928	2936	4393	2936	928	159	17	1	0	12475

a−g ↦ houses

Heather(a−g)
Lavender(a−g)

is the number of houses of the seals with

a and gravity g. (See triangle pair SlopedHeather.)