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

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

A118999 Number of real n X n symmetric (+1,-1) matrices with negative permanent.

Original entry on oeis.org

1, 0, 32, 240, 11904, 533568, 134217728, 22741568512, 16885168208896
Offset: 1

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A118988, A118997, A118999, A118993, A118994, A118995, A119001, A119010.

Formula

a(n) = A118993(n) - A118995(n). For odd n, a(n) = A118995(n) = A118993(n)/2. - Max Alekseyev, Jun 18 2025

Extensions

a(1) corrected and a(8)-a(9) added by Max Alekseyev, Jun 18 2025

A119001 Minimal permanent of real n X n symmetric (+1,-1) matrices.

Original entry on oeis.org

-1, 0, -6, -8, -120, -96, -5040, -4320, -362880
Offset: 1

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A118988, A118993, A118995, A118999, A119000, A119010.

Formula

For odd n, a(n) = -n!. - Max Alekseyev, Jun 18 2025

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

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A086906, A088672, A118988, A118989, A118990, A118993, A118995, A118999, A119001.

Extensions

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

A118991 Number of real n X n symmetric (0,1) matrices with nonzero permanent.

Original entry on oeis.org

1, 5, 39, 753, 25887, 1842241, 247531775, 65994415105, 34412945590783
Offset: 1

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A086899, A118986, A118989, A118993, A119009.

Formula

a(n) = 2^(n(n+1)/2) - A118989(n) = 2^A000217(n) - A118989(n) = A006125(n+1) - A118989(n). - Max Alekseyev, Apr 22 2010; corrected by Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 26 2010

Extensions

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

A118992 Number of real n X n invertible symmetric (+1,-1) matrices.

Original entry on oeis.org

2, 4, 32, 512, 16896, 1190144, 163899904, 46195853312, 25585116626944, 28281621931343872
Offset: 1

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A056990, A086899, A056989, A118990, A118993, A118994, A118997.

Formula

a(n) = 2^(n*(n+1)/2) - A118990(n) = A118994(n) + A118997(n). - Max Alekseyev, Jun 12 2025

Extensions

a(8)-a(10) from Max Alekseyev, Jun 17 2025
Showing 1-7 of 7 results.

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