A385386 -id:A385386 - cp's OEIS frontend

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

Pontus von Brömssen, Jun 27 2025

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.

			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  ?

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

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

A385387 Number of polysticks, i.e., connected nonempty subsets of edges, of the n X n flat torus, up to cyclic shifts and reflections of rows and columns.

Original entry on oeis.org

3, 40, 6432, 43918404

Offset: 1

Pontus von Brömssen, Jun 27 2025

Main diagonal of A385386.
Row sums of A385388.
Cf. A385382 (polyominoes), A385389 (interchange of rows and columns of the torus allowed).

cp's OEIS Frontend

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.

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A385387 Number of polysticks, i.e., connected nonempty subsets of edges, of the n X n flat torus, up to cyclic shifts and reflections of rows and columns.

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Author

Keywords

Crossrefs