Re primitive binary matrices?

[Brendan McKay]

* N. J. A. Sloane <njas at research.att.com> [030822 23:55]:
> 2.  Yuval Dekel <dekelyuval at hotmail.com> asks if these two
> sequences are in the OEIS:
> 
> Symmetric invertible 0,1 matrices (over the reals)
> Symmetric invertible 0,1 matrices (over GF(2))

There is an exact formula (or recurrence) for the second class.  I don't
remember where it is but the reference and a generalisation can be found in
R. P. Brent and B. D. McKay, Determinants of random symmetric matrices
 over $Z_m$,  Ars Combinatoria, 26-A (1988) 57--64.

Brendan.