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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. 0

%I

%S 1,2,4,10,24,62,158,410,1064,2774,7236,18908,49428,129286,338254,

%T 885188,2316766,6064184,15874084,41555086,108785772,284792646,

%U 745574864,1951901064,5110072712,13378217392,35024400076,91694660704,240059002292

%N 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 Column sums of the triangle in A121552.

%D E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29- 42.

%F 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 a(2)=2 because the only deco polyominoes of area 2 are the vertical and horizontal dominoes.

%p 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 Cf. A121552.

%K nonn

%O 1,2

%A _Emeric Deutsch_, Aug 16 2006

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Last modified July 23 12:19 EDT 2021. Contains 346259 sequences. (Running on oeis4.)