A369830 a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix using the integers 1 to n.

1, 1, 2, 5, 22, 97, 613, 4749, 38493, 353684

Offset

0,3

Links

Table of n, a(n) for n=0..9.

Wikipedia, Toeplitz Matrix.

Formula

a(n) <= A000142(n).

Mathematica

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

Prog

(Python)
from itertools import permutations
from sympy import Matrix
def A369830(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).det() for p in permutations(range(1, n+1))}) # Chai Wah Wu, Feb 12 2024

Crossrefs

Cf. A000142, A350953, A350954, A356865.

Cf. A369831, A369832, A369833, A369834, A369835.

Sequence in context: A371609 A030222 A362790 * A056840 A321608 A241345

Adjacent sequences: A369827 A369828 A369829 * A369831 A369832 A369833

Keyword

nonn,hard,more

Author

Stefano Spezia, Feb 03 2024

Status

approved