A351147 -id:A351147 - cp's OEIS frontend

A351609 Maximal absolute value of the determinant of an n X n symmetric matrix using the integers 1 to n*(n + 1)/2.

1, 1, 7, 152, 7113, 745285, 94974369

Offset: 0

Stefano Spezia, Feb 14 2022

Upper bounds for the next terms can be found by considering all possibilities of choosing matrix entries on the diagonal and applying Gasper's determinant theorem (see references in A085000): a(7) <= 22475584128, a(8) <= 6634478203404, a(9) <= 2647044512044258. - Hugo Pfoertner, Feb 18 2022

			a(3) = 152:
   2    4    6
   4    5    1
   6    1    3
a(4) = 7113:
   2    6    8    9
   6    5   10    1
   8   10    3    4
   9    1    4    7

Cf. A000217, A351147, A351148, A351153.

Cf. A085000, A180128, A350931, A350933, A350954, A350956.

a(n) = max(abs(A351147(n)), A351148(n)). - Hugo Pfoertner, Feb 16 2022

a(5)-a(6) from Hugo Pfoertner, Feb 16 2022

A358806 a(n) is the minimal determinant of an n X n symmetric matrix using all the integers from 0 to n*(n + 1)/2 - 1.

Original entry on oeis.org

1, 0, -4, -110, -5072, -488212, -86577891

Offset: 0

Stefano Spezia, Dec 02 2022

			a(2) = -4:
    [0, 2;
     2, 1]
a(3) = -110:
    [1, 3, 5;
     3, 4, 0;
     5, 0, 2]

Cf. A000217, A351147, A351153.

Cf. A358807 (maximal), A358808 (minimal permanent), A358809 (maximal permanent).

A351148 a(n) is the maximal determinant of a symmetric n X n matrix using the integers 1 to n*(n+1)/2.

Original entry on oeis.org

1, 5, 112, 7113, 745285, 90536348

Offset: 1

Hugo Pfoertner at the suggestion of Markus Sigg, Feb 15 2022

			a(2) = 5:
  [2, 1;
   1, 3]
.
a(3) = 112:
  [1, 5, 4;
   5, 3, 6;
   4, 6, 2]
.
a(4) = 7113:
  [ 3, 10,  4,  8;
   10,  5,  1,  6;
    4,  1,  7,  9;
    8,  6,  9,  2]
.
a(5) = 745285:
  [10, 12,  1,  4, 13;
   12,  6,  5, 15,  3;
    1,  5,  9, 11, 14;
    4, 15, 11,  7,  2;
   13,  3, 14,  2,  8]
.
a(6) = 90536348:
  [18,  1,  7, 14,  6, 15;
    1, 13,  5, 17,  8, 20;
    7,  5, 12,  2, 21, 16;
   14, 17,  2, 11, 19,  3;
    6,  8, 21, 19,  9,  4;
   15, 20, 16,  3,  4, 10]

Cf. A000217, A085000, A351147, A351609.

cp's OEIS Frontend

A351609 Maximal absolute value of the determinant of an n X n symmetric matrix using the integers 1 to n*(n + 1)/2.

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A358806 a(n) is the minimal determinant of an n X n symmetric matrix using all the integers from 0 to n*(n + 1)/2 - 1.

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A351148 a(n) is the maximal determinant of a symmetric n X n matrix using the integers 1 to n*(n+1)/2.

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