Triangles Willow(Drop)
The diagonal of both triangles is Lotus.
| 🌊 triangle row sums Grass (A001146)
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
| 0
|
1 · 2 2
|
|
|
|
|
|
2
|
| 1
|
1 · 2 2
|
1 · 2 2
|
|
|
|
|
4
|
| 2
|
1 · 2 2
|
2 · 2 4
|
1 · 10 10
|
|
|
|
16
|
| 3
|
1 · 2 2
|
3 · 2 6
|
3 · 10 30
|
1 · 218 218
|
|
|
256
|
| 4
|
1 · 2 2
|
4 · 2 8
|
6 · 10 60
|
4 · 218 872
|
1 · 64594 64594
|
|
65536
|
| 5
|
1 · 2 2
|
5 · 2 10
|
10 · 10 100
|
10 · 218 2180
|
5 · 64594 322970
|
1 · 4294642034 4294642034
|
4294967296
|
|
| 💧 triangle row sums GrassDrop (~A111403)
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
| 0
|
1 · 2 2
|
|
|
|
|
|
2
|
| 1
|
0
|
1 · 2 2
|
|
|
|
|
2
|
| 2
|
0
|
1 · 2 2
|
1 · 10 10
|
|
|
|
12
|
| 3
|
0
|
1 · 2 2
|
2 · 10 20
|
1 · 218 218
|
|
|
240
|
| 4
|
0
|
1 · 2 2
|
3 · 10 30
|
3 · 218 654
|
1 · 64594 64594
|
|
65280
|
| 5
|
0
|
1 · 2 2
|
4 · 10 40
|
6 · 218 1308
|
4 · 64594 258376
|
1 · 4294642034 4294642034
|
4294901760
|
|
| (a, v) ↦ all
|
Willow(a, v)
WillowDrop(a, v)
|
is the number of BF with
|
arity
adicity
|
a and valency v.
|
| half
|
| 🌊 triangle HalfWillow row sums HalfGrass (~A058891)
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
| 0
|
1 · 1 1
|
|
|
|
|
|
1
|
| 1
|
1 · 1 1
|
1 · 1 1
|
|
|
|
|
2
|
| 2
|
1 · 1 1
|
2 · 1 2
|
1 · 5 5
|
|
|
|
8
|
| 3
|
1 · 1 1
|
3 · 1 3
|
3 · 5 15
|
1 · 109 109
|
|
|
128
|
| 4
|
1 · 1 1
|
4 · 1 4
|
6 · 5 30
|
4 · 109 436
|
1 · 32297 32297
|
|
32768
|
| 5
|
1 · 1 1
|
5 · 1 5
|
10 · 5 50
|
10 · 109 1090
|
5 · 32297 161485
|
1 · 2147321017 2147321017
|
2147483648
|
|
| 💧 triangle HalfWillowDrop row sums HalfGrassDrop (~A040996)
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
| 0
|
1 · 1 1
|
|
|
|
|
|
1
|
| 1
|
0
|
1 · 1 1
|
|
|
|
|
1
|
| 2
|
0
|
1 · 1 1
|
1 · 5 5
|
|
|
|
6
|
| 3
|
0
|
1 · 1 1
|
2 · 5 10
|
1 · 109 109
|
|
|
120
|
| 4
|
0
|
1 · 1 1
|
3 · 5 15
|
3 · 109 327
|
1 · 32297 32297
|
|
32640
|
| 5
|
0
|
1 · 1 1
|
4 · 5 20
|
6 · 109 654
|
4 · 32297 129188
|
1 · 2147321017 2147321017
|
2147450880
|
|
|
Triangles TurnedWillow(Drop)
Column 0 is Lotus(Drop).
The row sums without it are NonLotus(Drop).
| 🌊 triangle TurnedWillow row sums Grass
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
| 0
|
2
|
|
|
|
|
|
2
|
| 1
|
2
|
2
|
|
|
|
|
4
|
| 2
|
10
|
4
|
2
|
|
|
|
16
|
| 3
|
218
|
30
|
6
|
2
|
|
|
256
|
| 4
|
64594
|
872
|
60
|
8
|
2
|
|
65536
|
| 5
|
4294642034
|
322970
|
2180
|
100
|
10
|
2
|
4294967296
|
|
| 💧 triangle TurnedWillowDrop row sums GrassDrop
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
| 0
|
2
|
|
|
|
|
|
2
|
| 1
|
0
|
2
|
|
|
|
|
2
|
| 2
|
8
|
2
|
2
|
|
|
|
12
|
| 3
|
208
|
26
|
4
|
2
|
|
|
240
|
| 4
|
64376
|
842
|
54
|
6
|
2
|
|
65280
|
| 5
|
4294577440
|
322098
|
2120
|
92
|
8
|
2
|
4294901760
|
|
Triangles SmallTurnedWillow(Drop)
Column 0 is SmallLotus(Drop).
The row sums without it are SmallNonLotus(Drop).
| 🌊 triangle SmallTurnedWillow row sums SmallGrass
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
| 0
|
1
|
|
|
|
|
|
1
|
| 1
|
2
|
1
|
|
|
|
|
3
|
| 2
|
10
|
4
|
1
|
|
|
|
15
|
| 3
|
218
|
30
|
6
|
1
|
|
|
255
|
| 4
|
64594
|
872
|
60
|
8
|
1
|
|
65535
|
| 5
|
4294642034
|
322970
|
2180
|
100
|
10
|
1
|
4294967295
|
|
| 💧 triangle SmallTurnedWillowDrop row sums SmallGrassDrop
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
| 0
|
1
|
|
|
|
|
|
1
|
| 1
|
1
|
1
|
|
|
|
|
2
|
| 2
|
8
|
3
|
1
|
|
|
|
12
|
| 3
|
208
|
26
|
5
|
1
|
|
|
240
|
| 4
|
64376
|
842
|
54
|
7
|
1
|
|
65280
|
| 5
|
4294577440
|
322098
|
2120
|
92
|
9
|
1
|
4294901760
|
|
| (a, g) ↦ all
|
SmallTurnedWillow(a, g)
SmallTurnedWillowDrop(a, g)
|
is the number of BF with
|
arity
adicity
|
a and gravity g. (The contradiction with infinite gravity is not counted.).
|