A189566 Number of permutations p of 1,2,...,n satisfying |p(i+2)-p(i)|<>4 and |p(j+4)-p(j)|<>2 for all i=1..n-2, j=1..n-4.

1, 2, 6, 24, 60, 208, 1184, 7840, 51636, 410272, 3836456, 39971896, 455888312, 5717233896, 78164908748, 1153568477544, 18263732340736, 308795344195456, 5550690255143992, 105653899427070440, 2122307518838927952

Offset: 1

Author

Vaclav Kotesovec, Apr 23 2011

Keywords

• nonn
• hard
• more

Comments

a(n) is also the number of ways to place n nonattacking pieces rook + leaper[2,4] on an n X n chessboard.

Links

• V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech)

Crossrefs

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

Formula

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

Extensions

a(17)-a(21) from Max Alekseyev, Jul 28 2024