A189566 - OEIS

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.

%I #13 Jul 28 2024 16:57:33

%S 1,2,6,24,60,208,1184,7840,51636,410272,3836456,39971896,455888312,

%T 5717233896,78164908748,1153568477544,18263732340736,308795344195456,

%U 5550690255143992,105653899427070440,2122307518838927952

%N 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.

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

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens, kings, bishops and knights</a> (in English and Czech)

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

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

%K nonn,hard,more

%O 1,2

%A _Vaclav Kotesovec_, Apr 23 2011

%E a(17)-a(21) from _Max Alekseyev_, Jul 28 2024