A374281 a(n) is the maximal absolute value of the 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, 44, 946, 27495, 592100, 25369920, 1246207300, 55400732937

Offset: 0

Author

Stefano Spezia, Jul 02 2024

Keywords

• nonn
• hard
• more

Examples

			a(5) = 946:
  [0, 1, 4, 2, 3]
  [1, 0, 1, 4, 2]
  [4, 1, 0, 1, 4]
  [2, 4, 1, 0, 1]
  [3, 2, 4, 1, 0]
		

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A085750, A351609.

Cf. A085807 (minimal permanent), A374279 (minimal), A374280 (maximal), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).

Programs

Mathematica

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

Formula

a(n) = max(abs(A374279(n)), A374280(n)).