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.

A119004 Number of n X n real symmetric (0,1)-matrices having maximal determinant (=A119002(n)).

Original entry on oeis.org

1, 1, 1, 18, 160, 900, 2520, 36960, 393120, 15573600
Offset: 1

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Extensions

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

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

Views

Author

Wouter Meeussen, Aug 23 2003

Keywords

Examples

			For n = 2 the only example is the identity matrix.
		

Crossrefs

Programs

  • 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

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

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

Extensions

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

A119003 Maximal determinant of real n X n symmetric (+1,-1) matrices.

Original entry on oeis.org

1, 0, 4, 16, 48, 160, 576, 4096, 14336, 65536
Offset: 1

Views

Author

Giovanni Resta, May 08 2006

Keywords

Comments

Computation of the determinant of these two matrices:
{-1, -1, -1, -1, 1, 1, 1, -1},
{-1, 1, -1, 1, 1, 1, -1, 1},
{-1, -1, 1, 1, 1, -1, -1, -1},
{-1, 1, 1, 1, -1, 1, 1, -1},
{ 1, 1, 1, -1, 1, 1, -1, -1},
{ 1, 1, -1, 1, 1, -1, 1, -1},
{ 1, -1, -1, 1, -1, 1, -1, -1},
{-1, 1, -1, -1, -1, -1, -1, -1}
and
{-1, 1, 1, -1, 1, -1, 1, 1, 1},
{ 1, -1, 1, -1, 1, 1, 1, 1, -1},
{ 1, 1, 1, 1, 1, -1, -1, 1, -1},
{-1, -1, 1, 1, -1, 1, 1, -1, 1},
{ 1, 1, 1, -1, -1, -1, 1, -1, -1},
{-1, 1, -1, 1, -1, 1, 1, 1, -1},
{ 1, 1, -1, 1, 1, 1, 1, -1, 1},
{ 1, 1, 1, -1, -1, 1, -1, 1, 1},
{ 1, -1, -1, 1, -1, -1, 1, 1, 1}
shows that a(8) = A003433(8) = 4096 and a(9) = A003433(9) = 14336. - Jean-François Alcover, Nov 19 2017
a(n) = n^(n/2) once there exists a symmetric Hadamard matrix of order n. In particular, a(12) = 12^6, a(16) = 16^8, etc. - Max Alekseyev, Jun 17 2025

Crossrefs

Extensions

a(8) and a(9) from Jean-François Alcover, Nov 19 2017
a(10) from Max Alekseyev, Jun 17 2025

A119006 Number of n X n real symmetric (0,1)-matrices having minimal determinant (=A118998(n)).

Original entry on oeis.org

1, 3, 3, 8, 60, 1620, 840, 23520, 756000, 30996000
Offset: 1

Views

Author

Giovanni Resta, May 08 2006

Keywords

Crossrefs

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

Extensions

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

A351984 a(n) is the number of symmetric anti-Hadamard matrices of order n whose sum of the inverse squares of their singular values is maximal.

Original entry on oeis.org

1, 2, 6, 24, 120, 840, 5040
Offset: 1

Views

Author

Stefano Spezia, Feb 27 2022

Keywords

Comments

The sequence of the ratio a(n+1)/a(n) begins with 2, 3, 4, 5, 7, 6, ...
Is a(n+1)/a(n) integer for all n? If that is true, excluding the number 1, is the sequence of the ratio a(n+1)/a(n) a permutation of all other natural numbers?

Crossrefs

Showing 1-7 of 7 results.