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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.
3

%I #9 Mar 19 2017 16:23:40

%S 1,1,2,6,24,80,326,1566,9544,65036,518498,4750006,48830634,554929274,

%T 6926227324,93970452970,1377573324202

%N 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.

%C a(n) is also the number of ways to place n nonattacking pieces rook + leaper[3,4] 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, A189566, A189567.

%K nonn,more,hard

%O 0,3

%A _Vaclav Kotesovec_, Apr 23 2011