A369834 a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n-1.

1, 1, 2, 5, 23, 94, 614, 4628, 38243, 351024

Offset: 0

Author

Stefano Spezia, Feb 03 2024

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Toeplitz Matrix.

Crossrefs

Cf. A000142, A358323, A358324, A358325.

Cf. A369830, A369831, A369832, A369833, A369835.

Programs

Mathematica

a[n_] := CountDistinct[Table[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n - 1]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]

Python

from itertools import permutations
from sympy import Matrix
def A369834(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).det() for p in permutations(range(n))}) # Chai Wah Wu, Feb 11 2024

Formula

a(n) <= A000142(n).