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A359618 a(n) is the minimal absolute value of the determinant of a nonsingular n X n Hermitian Toeplitz matrix using all the integers 1, 2, ..., n and with off-diagonal elements purely imaginary.

%I A359618 #11 Jan 25 2023 02:54:30
%S A359618 1,1,3,9,16,21,20,17,131,62,1
%N A359618 a(n) is the minimal absolute value of the determinant of a nonsingular n X n Hermitian Toeplitz matrix using all the integers 1, 2, ..., n and with off-diagonal elements purely imaginary.
%H A359618 Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>
%e A359618 a(4) = 16:
%e A359618    [   1,   2*i,   4*i,  3*i;
%e A359618     -2*i,     1,   2*i,  4*i;
%e A359618     -4*i,  -2*i,     1,  2*i;
%e A359618     -3*i,  -4*i,  -2*i,    1 ]
%t A359618 a={1}; For[n=1, n<=8, n++, mn=Infinity; For[d=1, d<=n, d++, For[i=1, i<=(n-1)!, i++, If[0<(t=Abs[Det[ToeplitzMatrix[Join[{d}, I Part[Permutations[Drop[Range[n], {d}]], i]]]]])<mn, mn=t]]]; AppendTo[a, mn]]; a
%Y A359618 Cf. A348891, A358325.
%Y A359618 Cf. A359559, A359561.
%Y A359618 Cf. A359614 (minimal signed), A359615 (maximal signed), A359616 (minimal permanent), A359617 (maximal permanent).
%K A359618 nonn,hard,more
%O A359618 0,3
%A A359618 _Stefano Spezia_, Jan 21 2023