A366768 Array read by antidiagonals, where each row is the coordination sequence for the underlying graph of the polyominoids occurring in the corresponding row of A366766.

1, 0, 1, 0, 2, 1, 0, 2, 0, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 4, 1, 0, 2, 0, 2, 8, 6, 1, 0, 2, 0, 2, 12, 16, 0, 1, 0, 2, 0, 2, 16, 24, 0, 4, 1, 0, 2, 0, 2, 20, 32, 0, 8, 4, 1, 0, 2, 0, 2, 24, 40, 0, 12, 8, 8, 1, 0, 2, 0, 2, 28, 48, 0, 16, 12, 16, 0, 1

Offset: 1

Author

Pontus von Brömssen, Oct 22 2023

Keywords

• nonn
• tabl

Comments

The underlying graph of a given type of polyominoids has all possible cells as nodes and edges between cells that are connected (respecting which types of connections are allowed). See A366766 for details on how the allowed connections are specified and on the ordering of the rows.

Examples

			Array begins:
  n\k| 0  1  2   3   4   5   6   7   8   9   10   11
  ---+----------------------------------------------
   1 | 1  0  0   0   0   0   0   0   0   0    0    0
   2 | 1  2  2   2   2   2   2   2   2   2    2    2
   3 | 1  0  0   0   0   0   0   0   0   0    0    0
   4 | 1  2  2   2   2   2   2   2   2   2    2    2
   5 | 1  4  8  12  16  20  24  28  32  36   40   44
   6 | 1  6 16  24  32  40  48  56  64  72   80   88
   7 | 1  0  0   0   0   0   0   0   0   0    0    0
   8 | 1  4  8  12  16  20  24  28  32  36   40   44
   9 | 1  4  8  12  16  20  24  28  32  36   40   44
  10 | 1  8 16  24  32  40  48  56  64  72   80   88
  11 | 1  0  0   0   0   0   0   0   0   0    0    0
  12 | 1  2  2   2   2   2   2   2   2   2    2    2
  13 | 1  8 30  68 126 180 286 348 510 572  798  852
  14 | 1 10 46 106 190 298 430 586 766 970 1198 1450
  15 | 1  0  0   0   0   0   0   0   0   0    0    0
  16 | 1  4  8  12  16  20  24  28  32  36   40   44
  17 | 1  8 30  68 126 180 286 348 510 572  798  852
  18 | 1 12 50 110 194 302 434 590 770 974 1202 1454
		

Links

• Pontus von Brömssen, Python programs that relate row numbers and parameter sets.
• Wikipedia, Polyominoid.
• Index entries for coordination sequences.
• Index entries for sequences related to polyominoes.

Crossrefs

Cf. A366766, A366767.