A385388 Irregular triangle read by rows: T(n,k) is the number of polysticks of size k, i.e., connected subsets of k edges, of the n X n flat torus, up to cyclic shifts and reflections of rows and columns; 1 <= k <= 2*n^2.

2, 1, 2, 3, 6, 11, 8, 7, 2, 1, 2, 3, 10, 24, 76, 213, 522, 982, 1308, 1274, 972, 593, 288, 114, 38, 10, 2, 1, 2, 3, 10, 28, 104, 387, 1518, 5799, 21336, 73400, 230462, 644155, 1556484, 3151899, 5183442, 6823550, 7342196, 6639409, 5131834, 3433229, 1992710, 1007190, 440148, 166572, 53566, 14806, 3356, 682, 104, 20, 2, 1

Offset: 1

Author

Pontus von Brömssen, Jun 27 2025

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  2, 1;
  2, 3,  6, 11,  8,   7,   2,   1;
  2, 3, 10, 24, 76, 213, 522, 982, 1308, 1274, 972, 593, 288, 114, 38, 10, 2, 1;
  ...
		

Crossrefs

Cf. A385383 (polyominoes), A385387 (row sums), A385390 (interchange of rows and columns of the torus allowed).

Formula

T(n,k) <= 2*A385390(n,k), with equality if and only if k is odd.