A086900 Number of real n X n symmetric (0,1) matrices with positive determinant.
1, 1, 5, 338, 14186, 526876, 52658844, 28076946520, 18518751047608, 13637385623943256
Offset: 1
Examples
For n = 2 the only example is the identity matrix.
Programs
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Mathematica
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}]
Formula
a(n) = A086899(n) - A118996(n) = 2^(n*(n+1)/2) - A086906(n) - A118996(n). - Max Alekseyev, Jun 12 2025
Extensions
a(6)-a(7) from Giovanni Resta, May 08 2006
a(8)-a(10) from Max Alekseyev, Jun 17 2025