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Search: id:A121753
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| A121753 |
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Number of deco polyominoes of height n in which all columns end at an odd level. 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, 1, 2, 6, 16, 62, 230, 1114, 5268, 30702, 176226, 1201638, 8107464, 63339702, 491010102, 4324845834, 37867131900, 371275954758, 3623124865986, 39137296073094, 421150512316032, 4969568447400366, 58455531552960198
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OFFSET
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1,3
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COMMENT
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a(n)=A121698(n,0).
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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)=(1+2floor((n-2)/2))a(n-1)-[floor((n-1)/2)floor((n-2)/2)-1]a(n-2) for n>=3, a(1)=1, a(2)=1.
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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 and only the horizontal one has all of its columns ending at an odd level.
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MAPLE
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a[1]:=1: a[2]:=1: for n from 3 to 26 do a[n]:= (1+2*floor((n-2)/2))*a[n-1]-(floor((n-1)/2)*floor((n-2)/2)-1)*a[n-2] od: seq(a[n], n=1..26);
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CROSSREFS
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Cf. A121698, A121751.
Sequence in context: A093113 A150030 A150031 this_sequence A150032 A121749 A009386
Adjacent sequences: A121750 A121751 A121752 this_sequence A121754 A121755 A121756
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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 23 2006
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