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A110128 Number of permutations p of 1,2,...,n satisfying |p(i+2)-p(i)| not equal to 2 for all 0<i<n-1. 10
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; text; internal format)
OFFSET

0,3

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, Jun 16 2010]

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..35

Vaclav Kotesovec, Mathematica program for this sequence

Roberto Tauraso, The Dinner Table Problem: The Rectangular Case, INTEGERS, vol. 6 (2006), paper A11. arXiv:math/0507293.

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.

CROSSREFS

Cf. A089222, A002464, A117574.

Sequence in context: A192890 A062330 A133465 * A148279 A101061 A148280

Adjacent sequences:  A110125 A110126 A110127 * A110129 A110130 A110131

KEYWORD

nonn,nice,hard

AUTHOR

Roberto Tauraso, A. Nicolosi and G. Minenkov, Jul 13 2005

EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Vladeta Jovovic, Jan 01 2008

Terms a(33)-a(35) from Vaclav Kotesovec, Apr 20 2012

STATUS

approved

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Last modified April 20 06:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)