A385381 Triangle read by rows: T(n,k) is the number of polyominoes, i.e., connected nonempty subsets of square cells (or vertices), of the n X k flat torus, up to cyclic shifts and reflections of rows and columns; 1 <= k <= n.

1, 2, 5, 3, 10, 28, 4, 21, 102, 801, 5, 40, 382, 6790, 129550, 6, 86, 1788, 68569, 2694721

Offset: 1

Author

Pontus von Brömssen, Jun 27 2025

Keywords

• nonn
• tabl
• more

Comments

Two square cells are connected if they share an edge.

Subsets that differ by interchanging rows and columns (when n = k) are considered distinct. For example, there are two polyominoes of size 2 when 2 <= k <= n, one horizontal and one vertical. See A385384 for the analog of the main diagonal of this sequence in the case where such subsets are considered identical.

Examples

			Triangle begins:
  n\k| 1  2    3     4       5  6
  ---+---------------------------
  1  | 1
  2  | 2  5
  3  | 3 10   28
  4  | 4 21  102   801
  5  | 5 40  382  6790  129550
  6  | 6 86 1788 68569 2694721  ?
		

Links

• Pontus von Brömssen, Illustration for T(3,3).

Crossrefs

Cf. A385382 (main diagonal), A385384, A385386 (edge subsets).