A189271 Number of permutations p of 1,2,...,n satisfying |p(i+6)-p(i)|<>6 for all 1<=i<=n-6.

1, 2, 6, 24, 120, 720, 4800, 34752, 280512, 2528256, 25282560, 278323200, 3289036800, 42336448512, 589351062528, 8820501301248, 141215147788800, 2407845089203200, 43543159894318080, 832618225074748416, 16782891792284791296

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[6,6] on an n X n chessboard.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..24
• 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, A189256.

Column k=6 of A333706.

Formula

Asymptotic (R. Tauraso 2006, quadratic term V. Kotesovec 2011): a(n)/n! ~ (1 + 20/n + 168/n^2)/e^2.

Generally (for this sequence is d=6): 1/e^2*(1+4(d-1)/n+2d*(3d-4)/n^2+...).

Extensions

Terms a(23)-a(24) from Vaclav Kotesovec, Apr 21 2012