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A358325 a(n) is the minimal absolute value of determinant of a nonsingular n X n symmetric Toeplitz matrix using the integers 0 to n - 1.

%I A358325 #12 Nov 19 2022 21:07:48
%S A358325 1,3,12,2,11,10,5,4,1,4,1
%N A358325 a(n) is the minimal absolute value of determinant of a nonsingular n X n symmetric Toeplitz matrix using the integers 0 to n - 1.
%H A358325 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A358323%2B4%2B5.py">Python program</a>.
%H A358325 Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%e A358325 a(3) = 3:
%e A358325     [1, 0, 2;
%e A358325      0, 1, 0;
%e A358325      2, 0, 1]
%e A358325 a(4) = 12:
%e A358325     [3, 2, 1, 0;
%e A358325      2, 3, 2, 1;
%e A358325      1, 2, 3, 2;
%e A358325      0, 1, 2, 3]
%e A358325 a(5) = 2:
%e A358325     [0, 4, 1, 2, 3;
%e A358325      4, 0, 4, 1, 2;
%e A358325      1, 4, 0, 4, 1;
%e A358325      2, 1, 4, 0, 4;
%e A358325      3, 2, 1, 4, 0]
%t A358325 Table[Min[Select[Table[Abs[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n-1]]], i]]]], {i, n!}], Positive]], {n, 2, 9}]  (* Corrected by _Stefano Spezia_, Nov 17 2022 *)
%Y A358325 Cf. A356865.
%Y A358325 Cf. A358323 (minimal signed), A358324 (maximal signed), A358326 (minimal permanent), A358327 (maximal permanent).
%K A358325 nonn,hard,more
%O A358325 2,2
%A A358325 _Stefano Spezia_, Nov 09 2022
%E A358325 a(3), a(7), and a(10)-a(12) from _Lucas A. Brown_, Nov 16 2022