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A369833
a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix using the first n prime numbers.
7
1, 1, 1, 6, 24, 120, 720, 5040, 40320, 362880
OFFSET
0,4
FORMULA
a(n) <= A000142(n).
Conjectured e.g.f.: 1/(1 - x) - x^2/2.
MATHEMATICA
a[n_] := CountDistinct[Table[Permanent[ToeplitzMatrix[Part[Permutations[Prime[Range[n]]], i]]], {i, n !}]]; Join[{1}, Array[a, 9]]
PROG
(Python)
from itertools import permutations
from sympy import primerange, prime, Matrix
def A369833(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).per() for p in permutations(primerange(prime(n)+1))}) if n else 1 # Chai Wah Wu, Feb 11 2024
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Feb 03 2024
STATUS
approved