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

%I #24 Mar 30 2023 07:38:22

%S 1,1,2,1,6,5,1,12,27,14,1,20,85,112,42,1,30,205,492,450,132,1,42,420,

%T 1582,2565,1782,429,1,56,770,4172,10415,12562,7007,1430

%N Triangle read by rows: T(n,k) = number of column-convex polyominoes with perimeter n and k columns (1 <= k <= n).

%H M.-P. Delest, <a href="/A006026/a006026.pdf">Utilisation des Langages Algébriques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos</a>, Ph.D. Dissertation, Université Bordeaux I, May 1987. [Scanned copy, with permission. A very large file.] See Figure 8.

%H M.-P. Delest, <a href="/A006026/a006026_1.pdf">Utilisation des Langages Algébriques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos</a>, Ph.D. Dissertation, Université Bordeaux I, May 1987. (Annotated scanned copy of a small part of the thesis)

%H M.-P. Delest, <a href="http://dx.doi.org/10.1016/0097-3165(88)90071-4">Generating functions for column-convex polyominoes</a>, J. Combin. Theory Ser. A 48 (1988), no. 1, 12-31.

%H S. Dulucq, <a href="/A005819/a005819.pdf">Etude combinatoire de problèmes d'énumeration, d'algorithmique sur les arbres et de codage par des mots</a>, a thesis presented to L'Université De Bordeaux I, 1987. (Annotated scanned copy)

%e Triangle begins:

%e 1,

%e 1,2,

%e 1,6,5,

%e 1,12,27,14,

%e 1,20,85,112,42,

%e 1,30,205,492,450,132,

%e 1,42,420,1582,2565,1782,429,

%e 1,56,770,4172,10415,12562,7007,1430,

%e ...

%Y Row sums are A006026.

%K nonn,tabl,more

%O 1,3

%A _N. J. A. Sloane_, Jun 24 2015