A306714 Permanent of the circulant matrix whose first row is given by the binary expansion of n.

0, 1, 1, 2, 1, 2, 2, 6, 1, 2, 4, 9, 2, 9, 9, 24, 1, 2, 2, 13, 2, 13, 13, 44, 2, 13, 13, 44, 13, 44, 44, 120, 1, 2, 4, 20, 8, 17, 17, 80, 4, 17, 36, 82, 17, 80, 82, 265, 2, 20, 17, 80, 17, 82, 80, 265, 20, 80, 82, 265, 80, 265, 265, 720, 1, 2, 2, 31, 2, 24, 24

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..8191

Wikipedia, Circulant matrix

Wikipedia, Permanent (mathematics)

Index entries for sequences related to binary expansion of n

Formula

a(n) = 1 <=> n in { A000079 }.

a(n) = floor(log_2(2n))! for n in { A126646 }.

a(A000225(n)) = A000142(n) for n >= 1.

a(A000051(n)) = A040000(n).

a(A007283(n)) = A007395(n+1).

Example

The circulant matrix for n = 23 = 10111_2 is
  [1 0 1 1 1]
  [1 1 0 1 1]
  [1 1 1 0 1]
  [1 1 1 1 0]
  [0 1 1 1 1] and has permanent 44, thus a(23) = 44.
a(10) = 4 != a(12) = 2 although 10 = 1010_2 and 12 = 1100_2 have the same number of 0's and 1's.

Maple

a:= n-> (l-> LinearAlgebra[Permanent](Matrix(nops(l),
         shape=Circulant[l])))(convert(n, base, 2)):
seq(a(n), n=0..100);

Crossrefs

Cf. A000051, A000079, A000142, A000225, A007283, A007395, A008305, A040000, A113473, A126646, A306595.

Sequence in context: A364872 A284002 A093659 * A200745 A067541 A054706

Adjacent sequences: A306711 A306712 A306713 * A306715 A306716 A306717

Keyword

nonn,base

Author

Alois P. Heinz, Mar 05 2019

Status

approved