A259333 Triangle read by rows: T(n,k) = number of column-convex polyominoes with bond-perimeter 2*n+2 and k columns (1 <= k <= n).

1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 37, 16, 1, 1, 25, 105, 106, 25, 1, 1, 36, 240, 446, 245, 36, 1

Offset: 1

Author

N. J. A. Sloane, Jun 24 2015

Keywords

• nonn
• tabl
• more

Examples

			Triangle begins:
1,
1,1,
1,4,1,
1,9,9,1,
1,16,37,16,1,
1,25,105,106,25,1,
1,36,240,446,245,36,1,
...
		

Links

• M.-P. Delest, Utilisation des Langages Algébriques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos, Ph.D. Dissertation, Université Bordeaux I, May 1987. [Scanned copy, with permission. A very large file.] See Figure 9.
• M.-P. Delest, Utilisation des Langages Algébriques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos, Ph.D. Dissertation, Université Bordeaux I, May 1987. (Annotated scanned copy of a small part of the thesis)
• M.-P. Delest, Generating functions for column-convex polyominoes, J. Combin. Theory Ser. A 48 (1988), no. 1, 12-31.
• S. Dulucq, Etude combinatoire de problèmes d'énumeration, d'algorithmique sur les arbres et de codage par des mots, a thesis presented to l'Université de Bordeaux I, 1987. (Annotated scanned copy)

Crossrefs

Row sums are A006027.

Formula

There is an explicit formula for T(n,k) - see Delest (1987), Theorem 24.