A374620 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 first n-1 primes off-diagonal.

1, 1, 1, 2, 6, 24, 120, 717, 5040, 40314, 362874

Offset: 0

Author

Stefano Spezia, Jul 14 2024

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A000142, A369832.

Cf. A374386, A374387, A374388, A374389.

Cf. A374617, A374618, A374619, A374621.

Programs

Mathematica

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

Formula

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