A374280 a(n) is the maximal determinant 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, 28, 282, 27495, 581268, 17344692, 1246207300, 33366771123

Offset: 0

Author

Stefano Spezia, Jul 02 2024

Keywords

• sign
• hard
• more

Examples

			a(5) = 282:
  [0, 3, 4, 2, 1]
  [3, 0, 3, 4, 2]
  [4, 3, 0, 3, 4]
  [2, 4, 3, 0, 3]
  [1, 2, 4, 3, 0]
		

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A085750, A358324.

Cf. A085807 (minimal permanent), A374279 (minimal), A374281 (maximal absolute value), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).

Programs

Mathematica

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