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

0,3

Comments

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

Links

Table of n, a(n) for n=0..6.

Formula

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

Example

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

Crossrefs

Cf. A000217, A351147, A351148, A351153.

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

Sequence in context: A171410 A277122 A351147 * A305686 A356739 A006761

Adjacent sequences: A351606 A351607 A351608 * A351610 A351611 A351612

Keyword

nonn,hard,more

Author

Stefano Spezia, Feb 14 2022

Extensions

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

Status

approved