login
Number of real n X n invertible symmetric (0,1) matrices.
5

%I #10 Mar 30 2012 18:37:43

%S 1,4,32,528,18596,1280468,180452552

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

%H <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>

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

%t 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}]

%Y Cf. A086900, A086906, A118991.

%K nonn,more

%O 1,2

%A _Wouter Meeussen_ Aug 23, 2003.

%E a(6) and a(7) from _Giovanni Resta_, May 08 2006