A189284 Number of permutations p of 1,2,...,n satisfying p(i+5)-p(i)<>5 for all 1<=i<=n-5.

1, 1, 2, 6, 24, 120, 696, 4572, 34260, 290328, 2751480, 28686024, 328764732, 4106158164, 55495145304, 806797105320, 12554890849992, 208164423163908, 3663256621120548, 68188490015132040, 1338490745511631080, 27630826605742438968

Offset: 0

Author

Vaclav Kotesovec, Apr 19 2011

Keywords

• nonn
• hard

Comments

a(n) is also number of ways to place n nonattacking pieces rook + semi-leaper[5,5] on an n X n chessboard.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..26 (Updated Jan 19 2019)
• Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 644.
• Vaclav Kotesovec, Mathematica program for this sequence
• George Spahn and Doron Zeilberger, Counting Permutations Where The Difference Between Entries Located r Places Apart Can never be s (For any given positive integers r and s), arXiv:2211.02550 [math.CO], 2022.

Crossrefs

Cf. A000255, A189281, A189282, A189283, A189256.

Formula

Asymptotics (V. Kotesovec, Mar 2011): a(n)/n! ~ (1 + 9/n + 20/n^2)/e.

Extensions

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