A119005 -id:A119005 - cp's OEIS frontend

A119003 Maximal determinant of real n X n symmetric (+1,-1) matrices.

1, 0, 4, 16, 48, 160, 576, 4096, 14336, 65536

Offset: 1

Giovanni Resta, May 08 2006

Computation of the determinant of these two matrices:
  {-1, -1, -1, -1,  1,  1,  1, -1},
  {-1,  1, -1,  1,  1,  1, -1,  1},
  {-1, -1,  1,  1,  1, -1, -1, -1},
  {-1,  1,  1,  1, -1,  1,  1, -1},
  { 1,  1,  1, -1,  1,  1, -1, -1},
  { 1,  1, -1,  1,  1, -1,  1, -1},
  { 1, -1, -1,  1, -1,  1, -1, -1},
  {-1,  1, -1, -1, -1, -1, -1, -1}
and
  {-1,  1,  1, -1,  1, -1,  1,  1,  1},
  { 1, -1,  1, -1,  1,  1,  1,  1, -1},
  { 1,  1,  1,  1,  1, -1, -1,  1, -1},
  {-1, -1,  1,  1, -1,  1,  1, -1,  1},
  { 1,  1,  1, -1, -1, -1,  1, -1, -1},
  {-1,  1, -1,  1, -1,  1,  1,  1, -1},
  { 1,  1, -1,  1,  1,  1,  1, -1,  1},
  { 1,  1,  1, -1, -1,  1, -1,  1,  1},
  { 1, -1, -1,  1, -1, -1,  1,  1,  1}
shows that a(8) = A003433(8) = 4096 and a(9) = A003433(9) = 14336. - Jean-François Alcover, Nov 19 2017
a(n) = n^(n/2) once there exists a symmetric Hadamard matrix of order n. In particular, a(12) = 12^6, a(16) = 16^8, etc. - Max Alekseyev, Jun 17 2025