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A128652
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Number of square permutations of length n.
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2
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1, 2, 6, 24, 104, 464, 2088, 9392, 42064, 187296, 828776, 3644912, 15937776, 69317984, 300009744, 1292654304, 5547021728, 23715100480, 101046014952, 429209373296, 1817975905456, 7680278380512, 32368750662320
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OFFSET
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1,2
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REFERENCES
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A. Bernini, F. Disanto, R. Pinzani and S. Rinaldi, Permutations defining convex permutominoes, Journal of Integer Sequences, 10 (2007) Article 07.9.7.
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LINKS
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Table of n, a(n) for n=1..23.
Michael Albert, Steve Linton, Nik Ruskuc, Vincent Vatter, Steve Waton, On convex permutations, Discrete Mathematics, vol.311, pp.715-722, (2011).
Sergey Kitaev and Jeffrey Remmel, Simple marked mesh patterns, Arxiv preprint arXiv:1201.1323, 2012
T. Mansour and S. Severini, Grid polygons from permutations and their enumeration by the kernel method
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FORMULA
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a(n) = 2*(n+2) * 4^(n-3) - 4*(2*n-5) * C(2*n-6,n-3) for n>=2, a(1)=1.
G.f.: x*(1-6*x+10*x^2-4*x^2*sqrt(1-4*x))/(1-4*x)^2 (See theorem 3.1 in Albert et. al. reference). [Joerg Arndt, Jun 21 2011]
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PROG
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(Pari) a(n) = if(n<=1, n, 2*(n+2) * 4^(n-3) - 4*(2*n-5) * binomial(2*n-6, n-3)); /* Joerg Arndt, Jun 21 2011 */
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CROSSREFS
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Sequence in context: A141253 A078486 A129817 * A152316 A177520 A152326
Adjacent sequences: A128649 A128650 A128651 * A128653 A128654 A128655
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, May 08 2007
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STATUS
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approved
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