%I #20 Oct 11 2022 00:54:50
%S 1,1,-3,-12,-100,-1749,-47600,-800681,-39453535,-1351201968,
%T -66984136299,-2938096403400,-235011452211680
%N Minimal determinant of an n X n symmetric Toeplitz matrix using the integers 1 to n.
%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A350953%2B4%2BA356865.py">A350953+4+A356865.py</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%e a(3) = -12:
%e 2 3 1
%e 3 2 3
%e 1 3 2
%e a(4) = -100:
%e 3 4 1 2
%e 4 3 4 1
%e 1 4 3 4
%e 2 1 4 3
%e a(5) = -1749:
%e 5 4 1 3 2
%e 4 5 4 1 3
%e 1 4 5 4 1
%e 3 1 4 5 4
%e 2 3 1 4 5
%o (Python)
%o from itertools import permutations
%o from sympy import Matrix
%o 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
%Y Cf. A307887, A350930, A350954 (maximal), A356865 (minimal nonzero absolute value).
%K sign,hard,more
%O 0,3
%A _Stefano Spezia_, Jan 27 2022
%E a(9) from _Alois P. Heinz_, Jan 27 2022
%E a(10)-a(12) from _Lucas A. Brown_, Sep 01 2022