A374618 a(n) is the number of distinct values 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, 1, 1, 2, 6, 22, 111, 695, 4920, 39881, 360242

Offset: 0

Author

Stefano Spezia, Jul 14 2024

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A000142, A369834.

Cf. A374279, A374280, A374281, A374282.

Cf. A374617, A374619, A374620, A374621.

Programs

Mathematica

a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]

Formula

a(n) <= (n-1)! for n > 0.