cp's OEIS Frontend

A189358 Number of permutations p of 1,2,...,n satisfying |p(i+1)-p(i)|<>3 and |p(j+3)-p(j)|<>1 for all i=1..n-1, j=1..n-3.

%I A189358 #28 Apr 04 2019 21:32:58
%S A189358 1,1,2,6,8,24,126,524,3072,22854,189646,1827114,19889946,238648524,
%T A189358 3131979014,44540692612,681114241416,11136984461270
%N A189358 Number of permutations p of 1,2,...,n satisfying |p(i+1)-p(i)|<>3 and |p(j+3)-p(j)|<>1 for all i=1..n-1, j=1..n-3.
%C A189358 a(n) is also the number of ways to place n nonattacking pieces rook + leaper[1,3] on an n X n chessboard (in fairy chess the leaper[1,3] is called a camel).
%H A189358 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 A189358 Asymptotic: a(n)/n! ~ 1/e^4.
%t A189358 A189358[n_] := Module[{p, c = 0, i = 1, q},
%t A189358    p=Permutations[Range[n]]; While[i <= Length[p], q = p[[i]]; i++;
%t A189358     If[AllTrue[Range[n - 1], Abs[q[[# + 1]] - q[[#]]] != 3 &] &&
%t A189358        AllTrue[Range[n - 3], Abs[q[[# + 3]] - q[[#]]] != 1 &], c++]]; c];
%t A189358 Table[A189358[n], {n, 0, 9}]  (* _Robert Price_, Apr 04 2019 *)
%Y A189358 Cf. A137774.
%K A189358 nonn,more,hard
%O A189358 0,3
%A A189358 _Vaclav Kotesovec_, Apr 23 2011
%E A189358 a(17) from _Alois P. Heinz_, Mar 19 2017