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A350953
Minimal determinant of an n X n symmetric Toeplitz matrix using the integers 1 to n.
9
1, 1, -3, -12, -100, -1749, -47600, -800681, -39453535, -1351201968, -66984136299, -2938096403400, -235011452211680
OFFSET
0,3
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).
Sequence in context: A133359 A102687 A202302 * A366668 A141535 A324313
KEYWORD
sign,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