A374283 a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.

1, 0, 1, 8, 256, 9978, 600052, 49036950, 5286564352, 725724599636

Offset: 0

Author

Stefano Spezia, Jul 02 2024

Keywords

• nonn
• hard
• more

Examples

			a(5) = 9978:
  [0, 4, 3, 2, 1]
  [4, 0, 4, 3, 2]
  [3, 4, 0, 4, 3]
  [2, 3, 4, 0, 4]
  [1, 2, 3, 4, 0]
		

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A085807 (minimal), A358327.

Cf. A374279, A374280, A374281, A374282.

Programs

Mathematica

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