A358327 a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1.

1, 0, 1, 12, 304, 12696, 778785, 64118596, 7014698888, 965862895732, 166105870928994, 34460169208369298

Offset: 0

Author

Stefano Spezia, Nov 09 2022

Keywords

• nonn
• hard
• more

Examples

			a(3) = 12:
    [2, 1, 0;
     1, 2, 1;
     0, 1, 2]
a(4) = 304:
    [2, 3, 1, 0;
     3, 2, 3, 1;
     1, 3, 2, 3;
     0, 1, 3, 2]
a(5) = 12696:
    [3, 4, 2, 1, 0;
     4, 3, 4, 2, 1;
     2, 4, 3, 4, 2;
     1, 2, 4, 3, 4;
     0, 1, 2, 4, 3]
		

Links

• Lucas A. Brown, A358326+7.sage.
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A351020.

Cf. A358323 (minimal determinant), A358324 (maximal determinant), A358326 (minimal).

Programs

Mathematica

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

Extensions

a(10) and a(11) from Lucas A. Brown, Nov 16 2022