A189565 Number of permutations p of 1,2,...,n satisfying |p(i+2)-p(i)|<>3 and |p(j+3)-p(j)|<>2 for all i=1..n-2, j=1..n-3.

1, 1, 2, 6, 12, 36, 174, 708, 4334, 31424, 263732, 2503296, 26844578, 316692056, 4090634212, 57274447458, 863488976620, 13936836270282, 239671043845414, 4373134317035736, 84359695604398332, 1715005778751119200, 36640921525885388532, 820633826572411883562, 19223689999433522041322

Offset

0,3

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[2,3] on an n X n chessboard (in fairy chess the leaper [2,3] is called a zebra).

Links

Table of n, a(n) for n=0..24.

Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 637.

Formula

Asymptotic: a(n)/n! ~ 1/e^4.

Crossrefs

Cf. A137774, A189358, A189563, A189564.

Sequence in context: A121404 A202337 A189854 * A074442 A162589 A225957

Adjacent sequences: A189562 A189563 A189564 * A189566 A189567 A189568

Keyword

nonn,hard,changed

Author

Vaclav Kotesovec, Apr 23 2011

Extensions

a(17)-a(24) from Martin Fuller, Mar 21 2026

Status

approved