A350931 Maximal determinant of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.

1, 1, 7, 105, 2294, 71753, 3051554, 175457984

Offset: 0

Author

Stefano Spezia, Jan 25 2022

Keywords

• nonn
• hard
• more

Comments

Also maximal absolute value of the determinant of an n X n Hankel matrix using the integers 1 to 2*n - 1. - Stefano Spezia, Dec 22 2023

Examples

			a(2) = 7:
   [3    1]
   [2    3]
a(3) = 105:
   [5    1    3]
   [4    5    1]
   [2    4    5]
		

Links

• Lucas A. Brown, A350930+1.py
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A322908, A323254, A350930 (minimal).

Programs

Python

from itertools import permutations
from sympy import Matrix
def A350931(n): return max(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).det() for p in permutations(range(1,2*n))) # Chai Wah Wu, Jan 27 2022

Extensions

a(5) from Alois P. Heinz, Jan 25 2022

a(6) from Pontus von Brömssen, Jan 26 2022

a(7) from Lucas A. Brown, Aug 28 2022