A350954 Maximal determinant of an n X n symmetric Toeplitz matrix using the integers 1 to n.

1, 1, 3, 15, 100, 3091, 49375, 1479104, 43413488, 1539619328, 64563673460, 2877312739624, 252631974548628

Offset: 0

Author

Stefano Spezia, Jan 27 2022

Keywords

• nonn
• hard
• more

Examples

			a(3) = 15:
    1    3    2
    3    1    3
    2    3    1
a(4) = 100:
    2    1    4    3
    1    2    1    4
    4    1    2    1
    3    4    1    2
a(5) = 3091:
    3    5    1    2    4
    5    3    5    1    2
    1    5    3    5    1
    2    1    5    3    5
    4    2    1    5    3
		

Links

• Lucas A. Brown, A350953+4+A356865.py
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A307887, A350931, A350953 (minimal), A356865 (minimal nonzero absolute value).

Programs

Python

from itertools import permutations
from sympy import Matrix
def A350954(n): return max(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).det() for p in permutations(range(1,n+1))) # Chai Wah Wu, Jan 27 2022

Extensions

a(9) from Alois P. Heinz, Jan 27 2022

a(10)-a(12) from Lucas A. Brown, Sep 01 2022