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

0,9

Links

Shalosh B. Ekhad and Doron Zeilberger, Table of n, a(n) for n = 0..100

D. Zeilberger, Automatic Enumeration of Generalized Ménage Numbers

Example

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

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 *)

Crossrefs

A diagonal of A008305.

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

Sequence in context: A364696 A308373 A183578 * A157062 A008273 A231240

Adjacent sequences: A184962 A184963 A184964 * A184966 A184967 A184968

Keyword

nonn

Author

Alois P. Heinz, Apr 20 2011

Status

approved