Triangle Sloe

Studies of Boolean functions
sequences related to seals
Pascal's triangle with multiplied columns

Compare triangle Ash.

Triangles Sloe(Drop)

The diagonal of both triangles is Ambrosia.

Pascal with columns multiplied by Ambrosia

馃寠    triangle    row sums Valerian
k
n
0 1 2 3 4 5 6 7 sums
0 11 1 1
1 11 1 11 1 2
2 11 1 21 2 12 2 5
3 11 1 31 3 32 6 16 6 16
4 11 1 41 4 62 12 46 24 120 20 61
5 11 1 51 5 102 20 106 60 520 100 178 78 264
6 11 1 61 6 152 30 206 120 1520 300 678 468 1300 300 1225
7 11 1 71 7 212 42 356 210 3520 700 2178 1638 7300 2100 11092 1092 5790

PascalDrop with columns multiplied by Ambrosia

馃挧    triangle    row sums ValerianDrop
k
n
0 1 2 3 4 5 6 7 sums
0 11 1 1
1   0 11 1 1
2   0 11 1 12 2 3
3   0 11 1 22 4 16 6 11
4   0 11 1 32 6 36 18 120 20 45
5   0 11 1 42 8 66 36 420 80 178 78 203
6   0 11 1 52 10 106 60 1020 200 578 390 1300 300 961
7   0 11 1 62 12 156 90 2020 400 1578 1170 6300 1800 11092 1092 4565

Triangles TurnedSloe(Drop)

馃寠    triangle TurnedSloe    row sums Valerian
k
n
0 1 2 3 4 5 6 7 sums
0 1 1
1 1 1 2
2 2 2 1 5
3 6 6 3 1 16
4 20 24 12 4 1 61
5 78 100 60 20 5 1 264
6 300 468 300 120 30 6 1 1225
7 1092 2100 1638 700 210 42 7 1 5790
馃挧    triangle TurnedSloeDrop    row sums ValerianDrop
k
n
0 1 2 3 4 5 6 7 sums
0 1 1
1 0 1 1
2 1 1 1 3
3 4 4 2 1 11
4 14 18 9 3 1 45
5 58 76 48 16 4 1 203
6 222 368 240 100 25 5 1 961
7 792 1632 1338 580 180 36 6 1 4565

The left columns are Ambrosia(Drop).

The first diagonals of TurnedSloeDrop are ones, natural numbers, square numbers, cubic minus square numbers (A045991). (Same as in Alder.)