A374241 a(n) is the maximal absolute value of the determinant 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, 0, 1, 40, 545, 13805, 526773, 18551951, 768561384, 31451535983, 1273675677456, 87868166035113, 7601760995500947, 664087819207293468

Offset: 0

Author

Stefano Spezia, Jul 01 2024

Keywords

• nonn
• hard
• more

Examples

			a(5) = 545:
  [1, 1, 4, 2, 3]
  [1, 1, 1, 4, 2]
  [4, 1, 1, 1, 4]
  [2, 4, 1, 1, 1]
  [3, 2, 4, 1, 1]
		

Links

• Lucas A. Brown, Python program.
• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A351609, A374139.

Cf. A374239 (minimal), A374240 (maximal), A374242 (minimal nonzero absolute value).

Programs

Mathematica

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

Formula

a(n) = max(abs(A374239(n)), A374240(n)).

Extensions

a(11)-a(14) from Lucas A. Brown, Oct 10 2024