A189282 Number of permutations p of 1,2,...,n satisfying p(i+3)-p(i)<>3 for all 1<=i<=n-3.

1, 1, 2, 6, 22, 98, 534, 3414, 25498, 217338, 2080990, 22076030, 256888218, 3252308706, 44497313158, 654139144158, 10281397705242, 172033123244330, 3052895403376110, 57266799403366334, 1132124282036449570, 23524895818926592242

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[3,3] on an n X n chessboard.

Links

• Christoph Koutschan, Table of n, a(n) for n = 0..48 (terms 0..30 from Vaclav Kotesovec, terms 31..36 from Manuel Kauers and Christoph Koutschan, terms 37..48 from George Spahn and Doron Zeilberger)
• 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, A117574.

Formula

Asymptotics: a(n)/n! ~ (1 + 5/n + 6/n^2)/e.