A184965 Number of permutations p of [n] such that (n-p(i)+i) mod n >= 6 for all i.

1, 0, 0, 0, 0, 0, 0, 1, 2, 78, 888, 13909, 204448, 3182225, 51504968, 873224962, 15498424578, 287972983669, 5598118158336, 113756109812283, 2413723031593090, 53416658591208438, 1231458960862452472, 29538634475147637783, 736321207493996695072

Offset: 0

Author

Alois P. Heinz, Apr 20 2011

Keywords

• nonn

Examples

			a(8) = 2: (2,3,4,5,6,7,8,1), (3,4,5,6,7,8,1,2).
		

Links

• Shalosh B. Ekhad and Doron Zeilberger, Table of n, a(n) for n = 0..100
• D. Zeilberger, Automatic Enumeration of Generalized Ménage Numbers

Crossrefs

A diagonal of A008305.

Cf. A000142, A000166, A000179, A000183, A004307.

Programs

Maple

with(LinearAlgebra):
a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)->
                     `if`(i-j<=0 and i-j>-6 or i-j>n-6, 0, 1)))):
seq(a(n), n=0..15);

Mathematica

a[n_] := Permanent[Table[If[i-j <= 0 && i-j > -6 || i-j > n-6, 0, 1], {i, 1, n}, {j, 1, n}]]; a[0] = 1; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 15}] (* Jean-François Alcover, Jan 07 2016, adapted from Maple *)