A189565 - OEIS

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.

%I #9 Mar 19 2017 16:19:37

%S 1,1,2,6,12,36,174,708,4334,31424,263732,2503296,26844578,316692056,

%T 4090634212,57274447458,863488976620

%N 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.

%C 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).

%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.

%K nonn,more,hard

%O 0,3

%A _Vaclav Kotesovec_, Apr 23 2011