A369834 - OEIS

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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.

7

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

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

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[Join[{0}, Range[n - 1]]], i]]], {i, n !}]]; Join[{1}, Array[a, 9]]

PROG

(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

CROSSREFS

Cf. A000142, A358323, A358324, A358325.

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

Sequence in context: A376156 A290887 A219889 * A100299 A371308 A038833

Adjacent sequences: A369831 A369832 A369833 * A369835 A369836 A369837

KEYWORD

nonn,hard,more

AUTHOR

Stefano Spezia, Feb 03 2024

STATUS

approved