A119001 -id:A119001 - cp's OEIS frontend

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

Index entries for sequences related to maximal determinants
N. A. Balonin, Y. N. Balonin, D. Z. Djokovic, D. A. Karbovskiy, M. B. Sergeev. Construction of symmetric Hadamard matrices, arXiv:1708.05098 [math.CO], 2017.
Wikipedia, Hadamard's maximal determinant problem.

Cf. A003433, A119002, A119001, A119005.

a(8) and a(9) from Jean-François Alcover, Nov 19 2017

a(10) from Max Alekseyev, Jun 17 2025

A119000 Minimal determinant of real n X n symmetric (+1,-1) matrices.

Original entry on oeis.org

-1, -2, -4, -16, -48, -160, -576, -2304, -14336, -73728

Offset: 1

Giovanni Resta, May 08 2006

Cf. A118998, A119001, A119003, A119007.

a(8)-a(10) from Max Alekseyev, Jun 17 2025

cp's OEIS Frontend

A118993 Number of real n X n symmetric (+1,-1) matrices with nonzero permanent.

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A118995 Number of real n X n symmetric (+1,-1) matrices with positive permanent.

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A118999 Number of real n X n symmetric (+1,-1) matrices with negative permanent.

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A119010 Number of symmetric n X n (+1,-1)-matrices over the reals with zero permanent.

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A118998 Minimal determinant of real n X n symmetric (0,1) matrices.

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

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A119000 Minimal determinant of real n X n symmetric (+1,-1) matrices.

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