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Search: id:A121691
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| A121691 |
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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. |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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Column sums of the triangle in A121552.
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REFERENCES
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E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29- 42.
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FORMULA
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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)].
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EXAMPLE
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a(2)=2 because the only deco polyominoes of area 2 are the vertical and horizontal dominoes.
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MAPLE
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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);
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CROSSREFS
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Cf. A121552.
Sequence in context: A055919 A006575 A138175 this_sequence A124499 A132220 A007874
Adjacent sequences: A121688 A121689 A121690 this_sequence A121692 A121693 A121694
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 16 2006
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