A369832 a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix using the first n prime numbers.

1, 1, 2, 6, 24, 116, 717, 5033, 40301, 362845

Offset: 0

Author

Stefano Spezia, Feb 03 2024

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A000142, A348891, A350955, A350956.

Cf. A369830, A369831, A369833, A369834, A369835.

Programs

Mathematica

a[n_] := CountDistinct[Table[Det[ToeplitzMatrix[Part[Permutations[Prime[Range[n]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]

Python

from itertools import permutations
from sympy import primerange, prime, Matrix
def A369832(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).det() for p in permutations(primerange(prime(n)+1))}) if n else 1 # Chai Wah Wu, Feb 11 2024

Formula

a(n) <= A000142(n).