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A164991
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Number of triangular involutions of n. A triangular involution is a square involution with at most three faces.
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0
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1, 1, 3, 6, 13, 26, 54, 108, 221, 442, 898, 1796, 3634, 7268, 14668, 29336, 59101, 118202, 237834, 475668, 956198, 1912396, 3841588, 7683176, 15425138, 30850276, 61908564, 123817128, 248377156, 496754312
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OFFSET
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1,3
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COMMENTS
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The sequence 2^(n+1)-C(n,floor(n/2)), which begins 1,3,6,... has Hankel transform (-1)^n*(2n+1) (A157142). [From Paul Barry, Nov 03 2010]
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REFERENCES
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F. Disanto,A. Frosini, S. Rinaldi, Square Involutions, Proceedings of Permutation Patterns, July, 13-17 2009, Florence.
T. Mansour, S. Severini, S. Grid polygons from permutations and their enumeration by the kernel method, 19-th Conference on Formal Power Series and Algebraic Combinatorics, Tianjin, China, July 2-6, 2007.
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LINKS
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Table of n, a(n) for n=1..30.
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FORMULA
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a(n)=2^(n-1)-C(n-2,(n-2)/2)
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CROSSREFS
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Cf. A128652, A128650
Sequence in context: A072762 A081254 A125049 * A213255 A215985 A215986
Adjacent sequences: A164988 A164989 A164990 * A164992 A164993 A164994
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KEYWORD
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easy,nonn
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AUTHOR
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Simone Rinaldi (rinaldi(AT)unisi.it), Sep 04 2009
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STATUS
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approved
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