A189568 Number of permutations p of 1,2,...,n satisfying |p(i+3)-p(i)|<>4 and |p(j+4)-p(j)|<>3 for all i=1..n-3, j=1..n-4.

1, 1, 2, 6, 24, 80, 326, 1566, 9544, 65036, 518498, 4750006, 48830634, 554929274, 6926227324, 93970452970, 1377573324202, 21681776874794, 364493926094022, 6515436596297818, 123361189739069826, 2465528488786858548, 51860386360621384438, 1144965844800298390500

Offset

0,3

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[3,4] on an n X n chessboard.

Links

Table of n, a(n) for n=0..23.

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

Formula

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

Crossrefs

Cf. A137774, A189358, A189563, A189564, A189565, A189566, A189567.

Sequence in context: A095110 A364819 A189858 * A002742 A048120 A322198

Adjacent sequences: A189565 A189566 A189567 * A189569 A189570 A189571

Keyword

nonn,hard,changed

Author

Vaclav Kotesovec, Apr 23 2011

Extensions

a(17)-a(23) from Martin Fuller, Mar 25 2026

Status

approved