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}]
A086906
Number of symmetric singular n X n (0,1) matrices over the reals.
Original entry on oeis.org
1, 4, 32, 496, 14172, 816684, 87982904, 18748545824, 7565600671504, 5940152086634096
Offset: 1
Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 19 2003
A118997
Number of real n X n symmetric (+1,-1) matrices with negative determinant.
Original entry on oeis.org
1, 4, 16, 80, 8448, 907904, 81949952, 13480664064, 12792558313472, 18963201072750592
Offset: 1
A118998
Minimal determinant of real n X n symmetric (0,1) matrices.
Original entry on oeis.org
0, -1, -2, -3, -5, -9, -32, -56, -128, -320
Offset: 1
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