A356865 Minimal absolute value of determinant of a nonsingular n X n symmetric Toeplitz matrix using the integers 1 to n.

1, 1, 3, 8, 12, 3, 13, 19, 5, 5, 1, 3, 1

Offset: 0

Author

Lucas A. Brown, Sep 01 2022

Keywords

• nonn
• hard
• more

Examples

			a(3) = 8:
    1  2  3
    2  1  2
    3  2  1
a(4) = 12:
    2  1  3  4
    1  2  1  3
    3  1  2  1
    4  3  1  2
a(5) = 3:
    1  5  2  3  4
    5  1  5  2  3
    2  5  1  5  2
    3  2  5  1  5
    4  3  2  5  1
		

Links

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

Crossrefs

Cf. A350953 (minimal signed), A350954 (maximal signed), A348891 (prime entries).

Programs

Python

from itertools import permutations
from sympy import Matrix
def A348891(n): return min(d for d in (abs(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).det()) for p in permutations(range(1,n+1))) if d > 0)