A117574 Total number of permutations p of [n] such that |p(i+3) - p(i)| is not equal to 3 for 1 <= i <= n-3.

1, 1, 2, 6, 20, 80, 384, 2240, 15424, 123456, 1110928, 11287232, 127016304, 1565107248, 20935873872, 301974271248, 4669727780624, 77046043259824, 1350585114106416, 25062108668100208, 490725684463001488, 10109820295907492304

Offset: 0

Author

James Sellers, Apr 27 2006

Keywords

• nonn
• hard

Comments

a(n) is also number of ways to place n nonattacking pieces rook + leaper[3,3] on an n X n chessboard.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..30
• 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.

Column k=3 of A333706.

Formula

Formula given in Tauraso reference.

Asymptotic (R. Tauraso 2006, quadratic term V. Kotesovec 2011): a(n)/n! ~ (1 + 8/n + 30/n^2)/e^2.

Extensions

Terms a(17)-a(28) from Vaclav Kotesovec, Apr 19 2011

Terms a(29)-a(30) from Vaclav Kotesovec, Apr 20 2012

a(0)=1 prepended by Alois P. Heinz, Feb 05 2023