A189285 Number of permutations p of 1,2,...,n satisfying p(i+6)-p(i)<>6 for all 1<=i<=n-6.

1, 1, 2, 6, 24, 120, 720, 4920, 37488, 319644, 3033264, 31784280, 364902480, 4538652840, 61102571376, 885045657564, 13722397569072, 226742901078120, 3977354871110160, 73816786920489720, 1444940702597713008, 29750236302549282948

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

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..24 (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, A189284, A189271.

Formula

Asymptotics (V. Kotesovec, Mar 2011): a(n)/n! ~ (1 + 11/n + 30/n^2)/e.

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

Extensions

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