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 1-5 of 5 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.
		

Crossrefs

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

A118986 Number of different values taken by the permanent of a symmetric real (0,1)-matrix of order n.

Original entry on oeis.org

1, 2, 3, 6, 14, 46, 176, 908, 5802, 44053
Offset: 0

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A006125 (number of symmetric real (0,1)-matrices of order (n-1)).

Extensions

a(8) from Minfeng Wang, Jun 12 2024
a(0)=1 prepended by Alois P. Heinz, Jun 12 2024
a(9) from Minfeng Wang, Jun 18 2024

A118987 Number of different values taken by the determinant of a symmetric real (+1,-1)-matrix of order n.

Original entry on oeis.org

1, 2, 2, 3, 5, 7, 11, 19, 40, 91, 214
Offset: 0

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Cf. A006125 (number of symmetric real (+1,-1)-matrices of order (n-1)).

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 16 2019
a(8) from Minfeng Wang, Jun 10 2024
a(9)-a(10) from Minfeng Wang, Jun 12 2024

A373915 Determinants of symmetric real {0,1}-matrices of order 9 that only occur as positive values.

Original entry on oeis.org

89, 94, 95, 97, 98, 99, 101, 102, 105, 110, 116, 125, 144
Offset: 1

Views

Author

Hugo Pfoertner, Jun 23 2024

Keywords

Comments

The non-occurrence of the corresponding negative determinants causes the difference A089472(9) - A118985(9) = 227 - 214 = 13.
A similar situation already occurs for 7 X 7 matrices, where the 3 determinant values -20, -24, -32 only occur with negative signs.

Crossrefs

A373916 Numbers that are the determinant of real {0,1}-matrices of order 10, but not of symmetric such matrices.

Original entry on oeis.org

253, 268, 274, 294, 304
Offset: 1

Views

Author

Hugo Pfoertner, Jun 25 2024

Keywords

Comments

This property also applies to the corresponding negative values.

Crossrefs

Showing 1-5 of 5 results.