A374239 a(n) is the minimal 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, 1, -545, -13805, -301184, -18551951, -352513176, -31451535983, -1209153784888, -87868166035113, -4204963833160760, -664087819207293468

Offset: 0

Author

Stefano Spezia, Jul 01 2024

Keywords

• sign
• 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. A350953, A374139.

Cf. A374240 (maximal), A374241 (maximal absolute value), A374242 (minimal nonzero absolute value).

Programs

Mathematica

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

Extensions

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