cp's OEIS Frontend

A121691 Number of deco polyominoes of area n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.

%I A121691 #2 Mar 30 2012 17:36:10
%S A121691 1,2,4,10,24,62,158,410,1064,2774,7236,18908,49428,129286,338254,
%T A121691 885188,2316766,6064184,15874084,41555086,108785772,284792646,
%U A121691 745574864,1951901064,5110072712,13378217392,35024400076,91694660704,240059002292
%N A121691 Number of deco polyominoes of area n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
%C A121691 Column sums of the triangle in A121552.
%D A121691 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29- 42.
%F A121691 G.f.=Sum(P(n,t), n=1..infinity), where P[n,t]=2t^n*product(2+sum(t^i, i=1..j), j=1..n-2) [in particular, P[1,t]=t; P[2,t]=2t^2; P[3,t]=2t^3*(2+t), P[4,t]=2t^4*(2+t)(2+t+t^2)].
%e A121691 a(2)=2 because the only deco polyominoes of area 2 are the vertical and horizontal dominoes.
%p A121691 P:=n->2*t^n*product(2+sum(t^i,i=1..j),j=1..n-2): g:=expand(simplify(sum(P(n),n=1..36))): seq(coeff(g,t,n),n=1..32);
%Y A121691 Cf. A121552.
%K A121691 nonn
%O A121691 1,2
%A A121691 _Emeric Deutsch_, Aug 16 2006