%I #28 Oct 23 2017 18:30:24

%S 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,

%T 36,1

%N Triangle read by rows: T(n,k) = number of column-convex polyominoes with bond-perimeter 2*n+2 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 9.

%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)

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

%e Triangle begins:

%e 1,

%e 1,1,

%e 1,4,1,

%e 1,9,9,1,

%e 1,16,37,16,1,

%e 1,25,105,106,25,1,

%e 1,36,240,446,245,36,1,

%e ...

%Y Row sums are A006027.

%K nonn,tabl,more

%O 1,5

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