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Search: id:A121747
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| A121747 |
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Number of columns of odd length in 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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| 1, 2, 8, 44, 262, 1938, 15600, 145086, 1461888, 16438446, 198598860, 2623055166, 36933441912, 560697617214, 9014444990964, 154698782105070, 2795947673216544, 53529558912435438, 1074325981318055676
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OFFSET
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1,2
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COMMENT
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a(n)=Sum(k*A121745(n,k), k=0..n).
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REFERENCES
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E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
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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Recurrence relation: a(n)=n*a[n-1]-d(n-1)+(n-1)!*floor(n/2) for n>=2, a(1)=1, where d(1)=1, d(2)=0, d(2n)=3!+5!+...+(2n-1)!, d(2n+1)=-d(2n).
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EXAMPLE
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a(2)=2 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having 0 and 2 columns of odd length, respectively.
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MAPLE
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d:=proc(n) if n=1 then 1 elif n=2 then 0 elif n mod 2 = 0 then add((2*j-1)!, j=2..n/2) else -d(n-1) fi end: a[1]:=1: for n from 2 to 22 do a[n]:=n*a[n-1]-d(n-1)+(n-1)!*floor(n/2) od: seq(a[n], n=1..22);
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CROSSREFS
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Cf. A121745, A121750.
Sequence in context: A018986 A128656 A047851 this_sequence A014508 A141147 A120928
Adjacent sequences: A121744 A121745 A121746 this_sequence A121748 A121749 A121750
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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 20 2006
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