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.

1, 1, 3, 9, 16, 21, 20, 17, 131, 62, 1

Offset

0,3

Links

Table of n, a(n) for n=0..10.

Wikipedia, Toeplitz Matrix

Example

a(4) = 16:
   [   1,   2*i,   4*i,  3*i;
    -2*i,     1,   2*i,  4*i;
    -4*i,  -2*i,     1,  2*i;
    -3*i,  -4*i,  -2*i,    1 ]

Mathematica

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

Crossrefs

Cf. A348891, A358325.

Cf. A359559, A359561.

Cf. A359614 (minimal signed), A359615 (maximal signed), A359616 (minimal permanent), A359617 (maximal permanent).

Sequence in context: A070066 A299636 A271491 * A214644 A184529 A338020

Adjacent sequences: A359615 A359616 A359617 * A359619 A359620 A359621

Keyword

nonn,hard,more

Author

Stefano Spezia, Jan 21 2023

Status

approved