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Search: id:A121582
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| A121582 |
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Number of cells in column 2 of all deco polyominoes of height 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
3
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| 0, 1, 7, 40, 252, 1837, 15259, 141798, 1455694, 16360387, 199845957, 2637020884, 37388864368, 566971338009, 9157693715407, 156975522127762, 2846305448882274, 54432896145210943, 1095019542858729769
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OFFSET
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1,3
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COMMENT
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a(n)=Sum(k*A121581(n,k),k=0..n-1).
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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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a(1)=0, a(2)=1, a(n)=[(2n-3)a(n-1)-(n-1)a(n-2)+(n-1)!(n-2)(n^2-3n+4)/2]/(n-2) for n>=3.
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EXAMPLE
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a(2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 0 and 1 cells in their second columns.
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MAPLE
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a:=proc(n) if n=1 then 0 elif n=2 then 1 else ((2*n-3)*a(n-1)-(n-1)*a(n-2)+(n-1)!*(n-2)*(n^2-3*n+4)/2)/(n-2) fi end: seq(a(n), n=1..22);
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CROSSREFS
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Cf. A121580, A121581, A121584.
Sequence in context: A099459 A051814 A154968 this_sequence A062727 A165397 A123747
Adjacent sequences: A121579 A121580 A121581 this_sequence A121583 A121584 A121585
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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 11 2006
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