A268371 Triangle read by rows: T(n,k) is the number of free polyominoes with width n and height 1<=k<=n.

1, 1, 2, 1, 6, 24, 1, 12, 181, 1051, 1, 30, 941, 21992, 238048, 1, 65, 4662, 228013, 9735647, 195284973, 1, 158, 23691, 2337694, 195616247, 15256715219, 577169894573

Offset: 1

Author

John Mason, Feb 03 2016

Keywords

• nonn
• tabl
• more

Comments

Superset of Craig Knecht's A268311.

Examples

			The first rows of the array are:
1;
1, 2;
1, 6, 24;
1, 12, 181, 1051;
...
T(4,3)=181 = 15+39+59+42+21+4+1: In the 4x3 square fit 15 6-ominoes, 39 7-ominoes, 59 8-ominoes, 42 9-ominoes, 21 10-ominoes, 4 11-ominoes or 1 12-omino. - _R. J. Mathar_, Jun 07 2020
		

Links

• Jean-Luc Manguin, Table of n, a(n) for n = 1..28
• R. J. Mathar, Corrigendum to "Polyomino Enumeration Results (Parkin et al, SIAM Fall Meeting 1967)" viXra:1905.0474 (2019)
• R. Parkin, L. J. Lander, and D. R. Parkin, Polyomino Enumeration Results, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy) page 9 (incorrect at n=15).
• Index entries for sequences related to polyominoes

Crossrefs

Cf. A268311 (right diagonal), A335711 (column n=2), A000105 (free polyominoes), A292357 (equival. for fixed polys).

Extensions

a(16)-a(28) from Jean-Luc Manguin, May 25 2020