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Search: id:A121751
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| A121751 |
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Number of deco polyominoes of height n in which all columns end at an even 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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+0
3
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| 0, 1, 2, 4, 14, 44, 194, 812, 4362, 22716, 144282, 897636, 6587454, 47632188, 396765018, 3268365228, 30471767658, 281641273164, 2906047413234, 29777551585092, 336912811924014, 3790278631556172, 46662633394518258
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OFFSET
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1,3
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COMMENT
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a(n)=A121697(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)=2floor((n-1)/2)a(n-1)-[floor((n-1)/2)floor((n-2)/2)-1]a(n-2) for n>=3, a(1)=0, 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 vertical one has all of its columns ending at an even level.
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MAPLE
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a[1]:=0: a[2]:=1: for n from 3 to 26 do a[n]:=2*floor((n-1)/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. A121697, A121753.
Sequence in context: A128750 A047152 A007866 this_sequence A014272 A070822 A101536
Adjacent sequences: A121748 A121749 A121750 this_sequence A121752 A121753 A121754
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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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