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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.
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%I #12 Nov 19 2022 21:07:48

%S 1,3,12,2,11,10,5,4,1,4,1

%N 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 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A358323%2B4%2B5.py">Python program</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>

%e a(3) = 3:

%e [1, 0, 2;

%e 0, 1, 0;

%e 2, 0, 1]

%e a(4) = 12:

%e [3, 2, 1, 0;

%e 2, 3, 2, 1;

%e 1, 2, 3, 2;

%e 0, 1, 2, 3]

%e a(5) = 2:

%e [0, 4, 1, 2, 3;

%e 4, 0, 4, 1, 2;

%e 1, 4, 0, 4, 1;

%e 2, 1, 4, 0, 4;

%e 3, 2, 1, 4, 0]

%t 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 Cf. A356865.

%Y Cf. A358323 (minimal signed), A358324 (maximal signed), A358326 (minimal permanent), A358327 (maximal permanent).

%K nonn,hard,more

%O 2,2

%A _Stefano Spezia_, Nov 09 2022

%E a(3), a(7), and a(10)-a(12) from _Lucas A. Brown_, Nov 16 2022