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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
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.
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
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 16 2006
STATUS
approved