A358324 a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1.

1, 0, 1, 8, 63, 2090, 36875, 1123653, 34292912, 1246207300, 53002204560, 2418538080316, 215120941720912

Offset: 0

Author

Stefano Spezia, Nov 09 2022

Keywords

• nonn
• hard
• more

Examples

			a(3) = 8:
    [0, 2, 1;
     2, 0, 2;
     1, 2, 0]
a(4) = 63:
    [1, 3, 2, 0;
     3, 1, 3, 2;
     2, 3, 1, 3;
     0, 2, 3, 1]
a(5) = 2090:
    [2, 4, 0, 1, 3;
     4, 2, 4, 0, 1;
     0, 4, 2, 4, 0;
     1, 0, 4, 2, 4;
     3, 1, 0, 4, 2]
		

Links

• Lucas A. Brown, Python program.
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A350954.

Cf. A358323 (minimal), A358325 (minimal nonzero absolute value), A358326 (minimal permanent), A358327 (maximal permanent).

Programs

Mathematica

Join[{1}, Table[Max[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