A086899 Number of real n X n invertible symmetric (0,1) matrices.

1, 4, 32, 528, 18596, 1280468, 180452552, 49970930912, 27618771417328, 30088644932329872

Offset: 1

Author

Wouter Meeussen, Aug 23 2003

Keywords

• nonn
• more

Examples

			For n = 2 the 4 matrices are 10/01, 01/10, 11/10, 01/11.
		

Links

• Index entries for sequences related to binary matrices

Crossrefs

Cf. A086900, A086906, A118991, A118985, A118992, A118993, A118996.

Programs

Mathematica

triamat[li_List] := (*see A086900*); Table[it=triamat/@IntegerDigits[Range[0, -1+2^(n(n+1)/2)], 2, n(n+1)/2]; Count[it, (q_)?MatrixQ/;(Det[q]=!=0)], {n, 5}]

Formula

a(n) = A086900(n) + A118996(n) = 2^(n*(n+1)/2) - A086906(n). - Max Alekseyev, Jun 12 2025

Extensions

a(6) and a(7) from Giovanni Resta, May 08 2006

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