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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified June 14 09:06 EDT 2021. Contains 345018 sequences. (Running on oeis4.)