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A121752
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Number of columns ending at an odd level 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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2
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1, 2, 7, 39, 235, 1746, 14166, 132408, 1341432, 15148080, 183764880, 2435607360, 34406268480, 523839899520, 8444375452800, 145266278169600, 2631329637350400, 50481429165619200, 1015073771517388800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)=Sum(k*A121697(n,k),k=0..n).
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REFERENCES
| 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
| Recurrence relation: a(n)=(2n-3)a(n-1)-(n-1)(n-3)a(n-2)+(n-2)!(n*floor(n/2)-(n-2)*floor((n-1)/2)-1); a[1]=1, a[2]=2.
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EXAMPLE
| a(2)=2 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having 0 and 2 columns ending at an odd level, respectively.
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MAPLE
| a[1]:=1: a[2]:=2: for n from 3 to 23 do a[n]:=(2*n-3)*a[n-1]-(n-1)*(n-3)*a[n-2]+(n-2)!*(n*floor(n/2)-(n-2)*floor((n-1)/2)-1) od: seq(a[n], n=1..23);
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CROSSREFS
| Cf. A121697, A121754.
Sequence in context: A106211 A014058 A119602 * A054133 A032118 A125660
Adjacent sequences: A121749 A121750 A121751 * A121753 A121754 A121755
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 23 2006
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