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.

1, 2, 4, 10, 24, 62, 158, 410, 1064, 2774, 7236, 18908, 49428, 129286, 338254, 885188, 2316766, 6064184, 15874084, 41555086, 108785772, 284792646, 745574864, 1951901064, 5110072712, 13378217392, 35024400076, 91694660704, 240059002292

Offset: 1

Author

Emeric Deutsch, Aug 16 2006

Keywords

• nonn

Comments

Column sums of the triangle in A121552.

Examples

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

References

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

Crossrefs

Cf. A121552.

Programs

Maple

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);

Formula

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)].