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

1,2

Comments

Column sums of the triangle in A121552.

References

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

Links

Table of n, a(n) for n=1..29.

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)].

Example

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

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);

Crossrefs

Cf. A121552.

Sequence in context: A246566 A230553 A138175 * A124499 A303840 A132220

Adjacent sequences: A121688 A121689 A121690 * A121692 A121693 A121694

Keyword

nonn

Author

Emeric Deutsch, Aug 16 2006

Status

approved