Lotus are the row sums of the weight triangle A163353. See here.
Lotus = Violet + HalfGrass
Sequences Lotus(Drop)
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|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7
|
| 🌊 Lotus (A000371)
|
2 |
2 |
10 |
218 |
64594 |
4294642034 |
18446744047940725978 |
340282366920938463334247399005993378250
|
| 💧 LotusDrop
|
2 |
0 |
8 |
208 |
64376 |
4294577440 |
18446744043646083944 |
340282366920938463315800654958052652272
|
| a ↦ dense
|
Lotus(a) is the number of dense BF with arity a.
|
| a ↦ gravity 0
|
|
| half
|
|
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7
|
| 🌊 HalfLotus (A003465)
|
1 |
1 |
5 |
109 |
32297 |
2147321017 |
9223372023970362989 |
170141183460469231667123699502996689125
|
| 💧 HalfLotusDrop
|
1 |
0 |
4 |
104 |
32188 |
2147288720 |
9223372021823041972 |
170141183460469231657900327479026326136
|
|
| row sums of ExLemon
|
| triangle ExLemon row sums Lotus (A000371)
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
| 0
|
1 · 2 2
|
|
|
|
|
|
2
|
| 1
|
0 · 2 0
|
1 · 2 2
|
|
|
|
|
2
|
| 2
|
0 · 2 0
|
1 · 2 2
|
1 · 8 8
|
|
|
|
10
|
| 3
|
0 · 2 0
|
1 · 2 2
|
4 · 8 32
|
1 · 184 184
|
|
|
218
|
| 4
|
0 · 2 0
|
1 · 2 2
|
13 · 8 104
|
11 · 184 2024
|
1 · 62464 62464
|
|
64594
|
| 5
|
0 · 2 0
|
1 · 2 2
|
40 · 8 320
|
90 · 184 16560
|
26 · 62464 1624064
|
1 · 4293001088 4293001088
|
4294642034
|
|
| row sums of SignedCedar
|
The absolute values are Pascal with columns multiplied by Grass.
| triangle SignedCedar row sums Lotus (A000371)
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
| 0
|
1 · 2 2
|
|
|
|
|
|
2
|
| 1
|
1 · 2 −2
|
1 · 4 4
|
|
|
|
|
2
|
| 2
|
1 · 2 2
|
2 · 4 −8
|
1 · 16 16
|
|
|
|
10
|
| 3
|
1 · 2 −2
|
3 · 4 12
|
3 · 16 −48
|
1 · 256 256
|
|
|
218
|
| 4
|
1 · 2 2
|
4 · 4 −16
|
6 · 16 96
|
4 · 256 −1024
|
1 · 65536 65536
|
|
64594
|
| 5
|
1 · 2 −2
|
5 · 4 20
|
10 · 16 −160
|
10 · 256 2560
|
5 · 65536 −327680
|
1 · 4294967296 4294967296
|
4294642034
|
|
Sequences SmallLotus(Drop)
SmallLotus differs from Lotus only in the first entry.
SmallLotus(Drop) are the left columns of SmallTurnedWillow(Drop).
|
|
0 |
1 |
2 |
3 |
4
|
| 🌊 SmallLotus
|
1 |
2 |
10 |
218 |
64594
|
| 💧 SmallLotusDrop
|
1 |
1 |
8 |
208 |
64376
|
| a ↦ gravity 0
|
SmallLotus(a)
SmallLotusDrop(a)
|
is the number of BF with
|
arity
adicity
|
a and gravity 0.
|