A369830 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

KEYWORD

nonn,hard,more

AUTHOR

STATUS

approved