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

1,2

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.

Links

Table of n, a(n) for n=1..20.

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

Example

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  ?

Crossrefs

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

Sequence in context: A138765 A378193 A097753 * A120860 A259971 A091809

Adjacent sequences: A385378 A385379 A385380 * A385382 A385383 A385384

Keyword

nonn,tabl,more

Author

Pontus von Brömssen, Jun 27 2025

Status

approved