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A358323 a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1.

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%I A358323 #12 Nov 16 2022 08:54:35
%S A358323 1,0,-1,-7,-60,-1210,-34020,-607332,-30448441,-1093612784,
%T A358323 -55400732937,-2471079070511,-197500419383964
%N A358323 a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1.
%H A358323 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A358323%2B4%2B5.py">A358323+4+5.py</a>.
%H A358323 Wikipedia, <a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%e A358323 a(3) = -7:
%e A358323     [1, 2, 0;
%e A358323      2, 1, 2;
%e A358323      0, 2, 1]
%e A358323 a(4) = -60:
%e A358323     [2, 3, 0, 1;
%e A358323      3, 2, 3, 0;
%e A358323      0, 3, 2, 3;
%e A358323      1, 0, 3, 2]
%e A358323 a(5) = -1210:
%e A358323     [4, 3, 0, 2, 1;
%e A358323      3, 4, 3, 0, 2;
%e A358323      0, 3, 4, 3, 0;
%e A358323      2, 0, 3, 4, 3;
%e A358323      1, 2, 0, 3, 4]
%t A358323 Join[{1}, Table[Min[Table[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n-1]]], i]]],{i,n!}]],{n,9}]]
%Y A358323 Cf. A350953.
%Y A358323 Cf. A358324 (maximal), A358325 (minimal nonzero absolute value), A358326 (minimal permanent), A358327 (maximal permanent).
%K A358323 sign,hard,more
%O A358323 0,4
%A A358323 _Stefano Spezia_, Nov 09 2022
%E A358323 a(10)-a(12) from _Lucas A. Brown_, Nov 16 2022