A189283 Number of permutations p of 1,2,...,n satisfying p(i+4)-p(i)<>4 for all 1<=i<=n-4.

1, 1, 2, 6, 24, 114, 628, 4062, 30360, 255186, 2414292, 25350954, 292378968, 3673917102, 49928069188, 729534877758, 11403682481112, 189862332575658, 3354017704180052, 62654508729565554, 1233924707891272728, 25550498290562247438

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[4,4] on an n X n chessboard.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..27 (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, A189255.

Formula

Asymptotics (V. Kotesovec, Mar 2011): a(n)/n! ~ (1 + 7/n + 12/n^2)/e.

Extensions

Terms a(26)-a(27) from Vaclav Kotesovec, Apr 20 2012