login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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

%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