A374278 a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

1, 1, 2, 18, 389, 14284, 798322, 62490160, 6519511313, 873036867840, 145856387327074

Offset: 0

Author

Stefano Spezia, Jul 02 2024

Keywords

• nonn
• hard
• more

Examples

			a(5) = 14284:
  [1, 4, 3, 2, 1]
  [4, 1, 4, 3, 2]
  [3, 4, 1, 4, 3]
  [2, 3, 4, 1, 4]
  [1, 2, 3, 4, 1]
		

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A351020, A374139, A374140 (minimal).

Cf. A374239, A374240, A374241, A374242.

Programs

Mathematica

a[0]=1; a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]], {i, (n-1)!}]]; Array[a, 11, 0]