cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

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

Views

Author

Wouter Meeussen, Aug 23 2003

Keywords

Examples

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

Links

Crossrefs

Cf. A086900, A086906, A118991, A118985, A118992, A118993, A118996.

Programs

  • Mathematica
    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}]

Formula

a(n) = A086900(n) + A118996(n) = 2^(n*(n+1)/2) - A086906(n). - Max Alekseyev, Jun 12 2025

Extensions

a(6) and a(7) from Giovanni Resta, May 08 2006
a(8)-a(10) from Max Alekseyev, Jun 17 2025

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

Views

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 19 2003

Keywords

Crossrefs

Cf. A046747, A086899, A086879, A086900, A118989, A118990, A118991, A118996, A119008, A119010.
Cf. A006125.

Formula

a(n) = 2^(n*(n+1)/2) - A086899(n).

Extensions

W. Edwin Clark computed the first entries.
a(6)-a(7) from Giovanni Resta, May 08 2006
a(8)-a(10) from Max Alekseyev, Jun 17 2025

A118995 Number of real n X n symmetric (+1,-1) matrices with positive permanent.

Original entry on oeis.org

1, 4, 32, 592, 11904, 1192384, 134217728, 41896879104, 16885168208896
Offset: 1

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A086900, A118988, A118999, A118993, A118994, A118999, A119001, A119010.

Formula

a(n) = A118993(n) - A118999(n). For odd n, a(n) = A118999(n) = A118993(n)/2. - Max Alekseyev, Jun 18 2025

Extensions

a(8)-a(9) from Max Alekseyev, Jun 18 2025

A118994 Number of real n X n symmetric (+1,-1) matrices with positive determinant.

Original entry on oeis.org

1, 0, 16, 432, 8448, 282240, 81949952, 32715189248, 12792558313472, 9318420858593280
Offset: 1

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A086900, A118992, A118995, A118997, A119003.

Programs

  • Maple
    F:= proc(n) local Q,q,X,x,t,A,ii,L,v;
  Q:= [[1,1],seq(seq([i,j],i=2..j),j=2..n)];
  q:= nops(Q);
  X:= [seq(x[q[1],q[2]],q=Q)];
  t:= 0:
  A:= Matrix(n,n,shape=symmetric,symbol=x);
  A[2..n,1]:= Vector(n-1,1);
  for ii from 0 to 2^q-1 do
    L:= map(s -> 2*s-1, convert(2^q+ii,base,2)[1..q]);
    v:= LinearAlgebra:-Determinant(subs(zip(`=`,X,L),A));
    if v > 0 then t:= t+1 fi
  od;
  2^(n-1)*t;
end proc:
seq(F(n),n=1..7); # Robert Israel, Apr 14 2016

Formula

a(n) = A118992(n) - A118997(n). For odd n, a(n) = A118997(n) = A118992(n)/2. - Max Alekseyev, Jun 12 2025

Extensions

a(8) from Robert Israel, Apr 17 2016
a(9)-a(10) from Max Alekseyev, Jun 17 2025

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

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A086899, A086900, A086906, A118997, A118998, A118999, A119006.

Formula

a(n) = A086899(n) - A086900(n) = 2^(n*(n+1)/2) - A086906(n) - A086900(n). - Max Alekseyev, Jun 12 2025

Extensions

a(8)-a(10) from Max Alekseyev, Jun 17 2025

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

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A086264, A086899, A086900, A086906, A118998, A119002, A119009.

Extensions

a(8)-a(10) from Max Alekseyev, Jun 17 2025

A080636 Number of real invertible (0,1) n X n matrices with (-1,0,1) inverses.

Original entry on oeis.org

1, 4, 28, 334, 7906
Offset: 1

Views

Author

Wouter Meeussen, Aug 25 2003

Keywords

Examples

			{{1,1,1,1,0},{1,1,1,0,1},{1,1,1,1,1},{1,0,1,1,0},{0,1,1,0,0}} qualifies since its inverse is
{{1,1,-1,0,-1},{1,0,0,-1,0},{-1,0,0,1,1},{0,-1,1,0,0},{-1,0,1,0,0}}

Programs

  • Mathematica
    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 && Union[Flatten[{Inverse[q], {-1, 0, 1}}]]==={-1, 0, 1}], {n, 5}]
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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