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

Author

Stefano Spezia, Feb 14 2022

Keywords

• nonn
• hard
• more

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

Examples

			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.

Formula

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

Extensions

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