This repository is for the purpose of supporting sequence submissions to OEIS when proofs are offered by way of program.
T(n,k) = number of free polyominoes with n cells, where the maximum number of cells in any row or column is k.
Collinearity considered for any line in the plane across tile centres
| k
n | 1 2 3 4 5 6 7 8
---------------------------------------------------------------------
1 | 1
2 | 0 1
3 | 0 1 1
4 | 0 2 2 1
5 | 0 0 9 2 1
6 | 0 0 18 13 3 1
7 | 0 0 37 48 19 3 1
8 | 0 0 62 200 77 25 4 1
T(n,k) = number of free polyominoes with n cells, where the maximum number of collinear tile centers on any line in the plane is k.
Collinearity only considered along rows or columns
| k
n | 1 2 3 4 5 6 7 8
---------------------------------------------------------------------
1 | 1
2 | 0 1
3 | 0 1 1
4 | 0 2 2 1
5 | 0 1 8 2 1
6 | 0 1 17 13 3 1
7 | 0 1 39 45 19 3 1
8 | 0 1 79 182 77 25 4 1
T(n,k) = number of free hexagon polyominoes with n cells, where the maximum number of cells on any lattice line is k.The term "lattice line" meaning a line running through the cell centres that is perpendicular to the hexagon cell sides.
| k
n | 1 2 3 4 5 6 7 8 9 10 Total
---------------------------------------------------------------------------------------
1 | 1 1
2 | 0 1 1
3 | 0 2 1 3
4 | 0 4 2 1 7
5 | 0 3 15 3 1 22
6 | 0 5 50 23 3 1 82
7 | 0 1 171 126 30 4 1 333
8 | 0 1 506 710 187 39 4 1 1448
9 | 0 1 1459 3520 1268 270 48 5 1 6572
10 | 0 1 3792 16617 7703 1948 364 59 5 1 30490
The T(4,2)=4 hexagon polyominoes are:
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T(n,k) = number of free hexagon polyominoes with n cells, where the maximum number of collinear cell centers on any line in the plane is k.
| k
n | 1 2 3 4 5 6 7 8 9 10 Total
---------------------------------------------------------------------------------------
1 | 1 1
2 | 0 1 1
3 | 0 2 1 3
4 | 0 4 2 1 7
5 | 0 2 16 3 1 22
6 | 0 3 52 23 3 1 82
7 | 0 0 169 129 30 4 1 333
8 | 0 0 477 740 187 39 4 1 1448
9 | 0 0 1245 3729 1274 270 48 5 1 6572
10 | 0 0 2750 17578 7785 1948 364 59 5 1 30490
The T(5,2)=2 hexagon polyominoes are:
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