A392133 a(n) is the permanent of the symmetric n X n matrix M defined by M(i,j) = gcd(2i-1,2j-1) for 1 <= i,j <= n.

1, 1, 4, 26, 232, 3352, 45712, 730608, 22696704, 467556288, 10714028160, 463127300352, 12739458645504, 500385722462208, 25305688040841216, 869717580695562240, 31881323261244063744, 2129706024448530235392, 157487079633163666145280, 6849538623833040704471040

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Example

a(3) = 26:
  [1, 1, 1]
  [1, 3, 1]
  [1, 1, 5]

Maple

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](
        Matrix(n, (i, j)-> igcd(2*i-1, 2*j-1)))):
seq(a(n), n=0..15);  # Alois P. Heinz, Feb 05 2026

Mathematica

a[n_]:=Permanent[Table[GCD[2i-1, 2j-1], {i, n}, {j, n}]]; Join[{1}, Array[a, 19]]

Prog

(PARI) a(n) = matpermanent(matrix(n, n, i, j, gcd(2*i-1, 2*j-1))); \\ Michel Marcus, Feb 06 2026

Crossrefs

Cf. A177066.

Sequence in context: A066224 A227917 A136227 * A346978 A000310 A054360

Adjacent sequences: A392130 A392131 A392132 * A392134 A392135 A392136

Keyword

nonn

Author

Stefano Spezia, Feb 05 2026

Status

approved