# Triangle Willow

| | valency gravity | strength depth |
| triangle | Willow | Poplar |
| diagonal | Lotus | Lily |
| difference | Orchid | Oxalis |
* Pascal's triangle with multiplied columns

## Triangles Willow$_{(Drop)}$

The diagonal of both triangles is Lotus.
🌊    triangle Willow    row sums Grass (A001146) :
| kn | 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 WillowDrop    row sums GrassDrop (~A111403) :
| kn | 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 |
half :
🌊    triangle HalfWillow    row sums HalfGrass (~A058891) :
| kn | 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) :
| kn | 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 Orchid$_{(Drop)}$.
🌊    triangle TurnedWillow    row sums Grass :
| kn | 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 :
| kn | 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 SmallOrchid$_{(Drop)}$.
🌊    triangle SmallTurnedWillow    row sums SmallGrass :
| kn | 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 :
| kn | 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 |