A189255 Number of permutations p of 1,2,...,n satisfying |p(i+4)-p(i)|<>4 for all 1<=i<=n-4.

1, 2, 6, 24, 108, 544, 3264, 23040, 176832, 1563392, 15536160, 171172224, 2066033472, 27146652480, 385447394880, 5878028516736, 95776238793504, 1660164417866304, 30496085473606944, 591661117634375040, 12087628978334638752

Offset: 1

Author

Vaclav Kotesovec, Apr 19 2011

Keywords

• nonn
• hard

Comments

a(n) is also number of ways to place n nonattacking pieces rook + leaper[4,4] on an n X n chessboard.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..27
• Vaclav Kotesovec, Non-attacking chess pieces, Sixth edition, p. 633, Feb 02 2013.
• Vaclav Kotesovec, Mathematica program for this sequence
• Roberto Tauraso, The Dinner Table Problem: The Rectangular Case, INTEGERS: Electronic Journal of Combinatorial Number Theory, Vol. 6 (2006), #A11.

Crossrefs

Cf. A002464, A110128, A117574.

Column k=4 of A333706.

Formula

Asymptotic (R. Tauraso 2006, quadratic term V. Kotesovec 2011): a(n)/n! ~ (1 + 12/n + 64/n^2)/e^2.

Extensions

Terms a(26)-a(27) from Vaclav Kotesovec, Apr 20 2012