A086899
Number of real n X n invertible symmetric (0,1) matrices.
Original entry on oeis.org
1, 4, 32, 528, 18596, 1280468, 180452552, 49970930912, 27618771417328, 30088644932329872
Offset: 1
For n = 2 the 4 matrices are 10/01, 01/10, 11/10, 01/11.
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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}]
A086900
Number of real n X n symmetric (0,1) matrices with positive determinant.
Original entry on oeis.org
1, 1, 5, 338, 14186, 526876, 52658844, 28076946520, 18518751047608, 13637385623943256
Offset: 1
For n = 2 the only example is the identity matrix.
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triamat[li_List] := Block[{len=Sqrt[8Length[li]+1]/2-1/2}, If[IntegerQ[len], Part[li, # ]& /@ Table[If[j>i, j(j-1)/2+i, i(i-1)/2+j], {i, len}, {j, len}], li]]; 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}]
A119010
Number of symmetric n X n (+1,-1)-matrices over the reals with zero permanent.
Original entry on oeis.org
0, 4, 0, 192, 8960, 371200, 0, 4081029120, 1414035671040
Offset: 1
A118996
Number of real n X n symmetric (0,1) matrices with negative determinant.
Original entry on oeis.org
0, 3, 27, 190, 4410, 753592, 127793708, 21893984392, 9100020369720, 16451259308386616
Offset: 1
A118989
Number of symmetric n X n (0,1)-matrices over the reals with zero permanent.
Original entry on oeis.org
1, 3, 25, 271, 6881, 254911, 20903681, 2725061631, 771426498049
Offset: 1
A118990
Number of symmetric singular n X n (+1,-1) matrices over the reals.
Original entry on oeis.org
0, 4, 32, 512, 15872, 907008, 104535552, 22523623424, 9599255461888, 7747175087620096
Offset: 1
A119008
Number of n X n real symmetric (0,1)-matrices with determinant = 1.
Original entry on oeis.org
1, 1, 4, 268, 9456, 301306, 24846368, 8946957244, 4175660906560, 2421067614753916
Offset: 1
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