A374279 a(n) is the minimal 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, 4, -44, -946, -8281, -592100, -25369920, -511563816, -55400732937

Offset: 0

Author

Stefano Spezia, Jul 02 2024

Keywords

• sign
• 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, A358323.

Cf. A085807 (minimal permanent), A374280 (maximal), A374281 (maximal absolute value), A374282 (minimal nonzero absolute value), A374283 (maximal permanent).

Programs

Mathematica

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