A189389 Number of permutations p of [n] such that (n-p(i)+i) mod n >= 5 for all i.

1, 0, 0, 0, 0, 0, 1, 2, 49, 484, 6208, 79118, 1081313, 15610304, 238518181, 3850864416, 65598500129, 1177003136892, 22203823852849, 439598257630414, 9117748844458320, 197776095898147080, 4479171132922158213, 105749311074795459594, 2598770324359627927649

Offset

0,8

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

Maple

with(LinearAlgebra):
a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)->
                     `if`(i-j<=0 and i-j>-5 or i-j>n-5, 0, 1)))):
seq(a(n), n=0..15);

Mathematica

a[n_] := Permanent[Table[If[i-j <= 0 && i-j > -5 || i-j > n-5, 0, 1], {i, 1, n}, {j, 1, n}]]; a[0] = 1; Table[a[n], {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: A297819 A297989 A028479 * A001568 A221134 A243720

Adjacent sequences: A189386 A189387 A189388 * A189390 A189391 A189392

Keyword

nonn

Author

Alois P. Heinz, Apr 20 2011

Status

approved