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

0,3

Links

Table of n, a(n) for n=0..12.

Lucas A. Brown, A350953+4+A356865.py

Wikipedia, Toeplitz Matrix

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A147664 A219779 A303651 * A196962 A074521 A074536

Adjacent sequences: A350951 A350952 A350953 * A350955 A350956 A350957

Keyword

nonn,hard,more

Author

Stefano Spezia, Jan 27 2022

Extensions

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

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

Status

approved