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A110128
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Number of permutations p of 1,2,...,n satisfying |p(i+2)-p(i)| not equal to 2 for all 0<i<n-1.
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11
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1, 1, 2, 4, 16, 44, 200, 1288, 9512, 78652, 744360, 7867148, 91310696, 1154292796, 15784573160, 232050062524, 3648471927912, 61080818510972, 1084657970877416, 20361216987032284, 402839381030339816, 8377409956454452732
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| When n is even: 1) Number of ways that n persons seated at a rectangular table with n/2 seats along the two opposite sides can be rearranged in such a way that neighbors are no more neighbors after the rearrangement. 2) Number of ways to arrange n kings on an n X n board, with 1 in each row and column, which are non-attacking with respect to the main four quadrants.
a(n) is also number of ways to place n nonattacking pieces rook + alfil on an n X n chessboard (Alfil is a leaper [2,2]) [From Vaclav Kotesovec (kotesovec(AT)chello.cz), Jun 16 2010]
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REFERENCES
| Roberto Tauraso, The Dinner Table Problem: The Rectangular Case, INTEGERS, vol. 6 (2006), paper A11.
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LINKS
| Vaclav Kotesovec, Table of n, a(n) for n = 0..32
Vaclav Kotesovec, Mathematica program for this sequence
Roberto Tauraso, The Dinner Table Problem: The Rectangular Case
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FORMULA
| A formula is given in the Tauraso reference.
Asymptotic (R. Tauraso 2006, quadratic term V. Kotesovec 2011): a(n)/n! ~ (1 + 4/n + 8/n^2)/e^2.
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CROSSREFS
| Cf. A089222, A002464, A117574.
Sequence in context: A192890 A062330 A133465 * A148279 A101061 A148280
Adjacent sequences: A110125 A110126 A110127 * A110129 A110130 A110131
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KEYWORD
| nonn
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AUTHOR
| R. Tauraso, A. Nicolosi and G. Minenkov (tauraso(AT)mat.uniroma2.it), Jul 13 2005
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Vladeta Jovovic, Jan 01 2008
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