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

0,3

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

Links

Table of n, a(n) for n=0..7.

Lucas A. Brown, A350930+1.py

Wikipedia, Toeplitz Matrix

Example

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

Prog

(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

Crossrefs

Cf. A322908, A323254, A350930 (minimal).

Sequence in context: A131869 A132867 A145666 * A344445 A238464 A360347

Adjacent sequences: A350928 A350929 A350930 * A350932 A350933 A350934

Keyword

nonn,hard,more

Author

Stefano Spezia, Jan 25 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

Status

approved