login
A369831
a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix using the integers 1 to n.
6
1, 1, 1, 6, 23, 120, 720, 5040, 40320, 362880
OFFSET
0,4
FORMULA
a(n) <= A000142(n).
Conjectured e.g.f.: 1/(1 - x) - x^2/2 - x^4/24.
MATHEMATICA
a[n_] := CountDistinct[Table[Permanent[ToeplitzMatrix[Part[Permutations[Range[n]], i]]], {i, n!}]]; Join[{1}, Array[a, 9]]
PROG
(Python)
from itertools import permutations
from sympy import Matrix
def A369831(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).per() 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