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.

1, 1, 2, 6, 8, 24, 126, 524, 3072, 22854, 189646, 1827114, 19889946, 238648524, 3131979014, 44540692612, 681114241416, 11136984461270

Offset: 0

Author

Vaclav Kotesovec, Apr 23 2011

Keywords

• nonn
• more
• hard

Comments

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).

Links

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

Crossrefs

Cf. A137774.

Programs

Mathematica

A189358[n_] := Module[{p, c = 0, i = 1, q},
   p=Permutations[Range[n]]; While[i <= Length[p], q = p[[i]]; i++;
    If[AllTrue[Range[n - 1], Abs[q[[# + 1]] - q[[#]]] != 3 &] &&
       AllTrue[Range[n - 3], Abs[q[[# + 3]] - q[[#]]] != 1 &], c++]]; c];
Table[A189358[n], {n, 0, 9}]  (* Robert Price, Apr 04 2019 *)

Formula

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

Extensions

a(17) from Alois P. Heinz, Mar 19 2017