A385386 Triangle read by rows: T(n,k) is the number of polysticks, i.e., connected nonempty subsets of edges, of the n X k flat torus, up to cyclic shifts and reflections of rows and columns; 1 <= k <= n.

3, 7, 40, 14, 225, 6432, 26, 1768, 255451, 43918404

Offset: 1

Author

Pontus von Brömssen, Jun 27 2025

Keywords

• nonn
• tabl
• more

Comments

Two edges are connected if they share a vertex.

Subsets that differ by interchanging rows and columns (when n = k) are considered distinct. For example, there are two distinct polysticks of size 1, one horizontal and one vertical. See A385389 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
  ---+------------------------
  1  |  3
  2  |  7   40
  3  | 14  225   6432
  4  | 26 1768 255451 43918404
		

Links

• Pontus von Brömssen, Illustration for T(3,2).

Crossrefs

Cf. A385381 (polyominoes), A385387 (main diagonal), A385389.