A189256 Number of permutations p of 1,2,...,n satisfying |p(i+5)-p(i)|<>5 for all 1<=i<=n-5.

1, 2, 6, 24, 120, 672, 4128, 28992, 231936, 2088960, 20434944, 221871360, 2645370624, 34344038400, 482103767040, 7269498483456, 117240911729664, 2013265377314688, 36665783917283328, 705762463906133760, 14313891805008665856

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[5,5] on an n X n chessboard.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..26
• 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, A189255.

Column k=5 of A333706.

Formula

Asymptotic (R. Tauraso 2006, quadratic term V. Kotesovec 2011): a(n)/n! ~ (1 + 16/n + 110/n^2)/e^2.

Extensions

Terms a(25)-a(26) from Vaclav Kotesovec, Apr 20 2012