A374390 a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.

1, 0, 4, 36, 1936, 144260, 31972988, 6800311204, 2560967581304, 975834087080060, 557171087172087364

Offset: 0

Author

Stefano Spezia, Jul 07 2024

Keywords

• nonn
• hard
• more

Examples

			a(5) = 144260:
  [0, 7, 5, 3, 2]
  [7, 0, 7, 5, 3]
  [5, 7, 0, 7, 5]
  [3, 5, 7, 0, 7]
  [2, 3, 5, 7, 0]
		

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A374345.

Cf. A374386, A374387, A374388, A374389.

Cf. A374068 (minimal permanent).

Programs

Mathematica

a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]