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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.
7
1, 1, 2, 5, 22, 97, 613, 4749, 38493, 353684
OFFSET
0,3
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
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Feb 03 2024
STATUS
approved