A350953 - OEIS

A350953

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

1, 1, -3, -12, -100, -1749, -47600, -800681, -39453535, -1351201968, -66984136299, -2938096403400, -235011452211680

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

EXAMPLE

a(3) = -12:

2 3 1

3 2 3

1 3 2

a(4) = -100:

3 4 1 2

4 3 4 1

1 4 3 4

2 1 4 3

a(5) = -1749:

5 4 1 3 2

4 5 4 1 3

1 4 5 4 1

3 1 4 5 4

2 3 1 4 5

PROG

(Python)

from itertools import permutations

from sympy import Matrix

def A350953(n): return min(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, A350930, A350954 (maximal), A356865 (minimal nonzero absolute value).

KEYWORD

sign,hard,more

AUTHOR

EXTENSIONS

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

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

STATUS

approved