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

1, 0, -1, -7, -60, -1210, -34020, -607332, -30448441, -1093612784, -55400732937, -2471079070511, -197500419383964

Offset: 0

Author

Stefano Spezia, Nov 09 2022

Keywords

• sign
• hard
• more

Examples

			a(3) = -7:
    [1, 2, 0;
     2, 1, 2;
     0, 2, 1]
a(4) = -60:
    [2, 3, 0, 1;
     3, 2, 3, 0;
     0, 3, 2, 3;
     1, 0, 3, 2]
a(5) = -1210:
    [4, 3, 0, 2, 1;
     3, 4, 3, 0, 2;
     0, 3, 4, 3, 0;
     2, 0, 3, 4, 3;
     1, 2, 0, 3, 4]
		

Links

• Lucas A. Brown, A358323+4+5.py.
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A350953.

Cf. A358324 (maximal), A358325 (minimal nonzero absolute value), A358326 (minimal permanent), A358327 (maximal permanent).

Programs

Mathematica

Join[{1}, Table[Min[Table[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n-1]]], i]]],{i,n!}]],{n,9}]]

Extensions

a(10)-a(12) from Lucas A. Brown, Nov 16 2022