A119002 Maximal determinant of real n X n symmetric (0,1) matrices.

1, 1, 1, 2, 3, 5, 9, 18, 56, 144, 320

Offset: 0

Author

Giovanni Resta, May 08 2006

Keywords

• nonn
• more

Comments

The determinant of this 8 X 8 matrix is a(8) = 56:

{0, 1, 1, 1, 0, 1, 0, 0},

{1, 0, 1, 1, 0, 1, 0, 0},

{1, 1, 0, 1, 0, 0, 1, 1},

{1, 1, 1, 0, 1, 0, 0, 1},

{0, 0, 0, 1, 1, 1, 0, 1},

{1, 1, 0, 0, 1, 1, 1, 0},

{0, 0, 1, 0, 0, 1, 1, 1},

{0, 0, 1, 1, 1, 0, 1, 0}

and the determinant of this 9 X 9 matrix is a(9) = 144:

{1, 1, 0, 1, 1, 0, 0, 1, 1},

{1, 1, 1, 1, 0, 1, 0, 0, 0},

{0, 1, 1, 1, 0, 0, 1, 1, 1},

{1, 1, 1, 0, 1, 0, 1, 0, 1},

{1, 0, 0, 1, 0, 1, 1, 0, 1},

{0, 1, 0, 0, 1, 1, 1, 1, 0},

{0, 0, 1, 1, 1, 1, 0, 0, 1},

{1, 0, 1, 0, 0, 1, 0, 1, 1},

{1, 0, 1, 1, 1, 0, 1, 1, 0}. - Jean-François Alcover, Nov 18 2017

Links

• Index entries for sequences related to maximal determinants

Crossrefs

Cf. A003432, A119003, A119004, A118998.

Formula

a(n) <= A003432(n).

Extensions

a(8) and a(9) from Jean-François Alcover, Nov 18 2017

a(0)=1 prepended by Alois P. Heinz, Nov 18 2017

a(10) from Max Alekseyev, Jun 17 2025