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Search: id:A121584
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| A121584 |
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Number of cells in columns 1 and 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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3
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| 1, 4, 18, 93, 569, 4074, 33336, 306035, 3111771, 34708944, 421407314, 5533007841, 78125977725, 1180594364966, 19012215609564, 325058642549919, 5880810783960431, 112243265407073100, 2254038189505807926
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OFFSET
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1,2
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COMMENT
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a(n)=Sum(A121583(n,k),k=1..2n-2) for n>=2. a(n)=A121580(n)+A121582(n)
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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)=1, a(2)=4, a(n)=[(2n-3)a(n-1)-(n-1)a(n-2)]/(n-2) + (1/2)(2n^3-9n^2+17n-16)(n-1)!/(n-2) for n>=3.
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EXAMPLE
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a(2)=4 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, each having a total of 2 cells in their first two columns.
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MAPLE
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a[1]:=1: a[2]:=4: for n from 3 to 22 do a[n]:=((2*n-3)*a[n-1]-(n-1)*a[n-2])/(n-2)+(1/2)*(2*n^3-9*n^2+17*n-16)*(n-1)!/(n-2) od: seq(a[n], n=1..22);
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CROSSREFS
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Cf. A121580, A121582, A121583.
Sequence in context: A081923 A020064 A123589 this_sequence A059227 A081103 A005777
Adjacent sequences: A121581 A121582 A121583 this_sequence A121585 A121586 A121587
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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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