A369943 a(n) is the number of distinct values of the permanent of an n X n Hankel matrix using the integers 1 to 2*n - 1.

1, 1, 2, 49, 2117, 156189, 16943487

Offset: 0

Author

Stefano Spezia, Feb 06 2024

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Hankel matrix.

Crossrefs

Cf. A350937, A350938.

Programs

Mathematica

a[n_] := CountDistinct[Table[Permanent[HankelMatrix[Join[Drop[per = Part[Permutations[Range[2 n - 1]], i], n],{Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]]

PARI

a(n) = my(v=[1..2*n-1], list=List()); forperm(v, p, listput(list, matpermanent(matrix(n, n, i, j, p[i+j-1])));); #Set(list); \\ Michel Marcus, Feb 08 2024

Python

from itertools import permutations
from sympy import Matrix
def A369943(n): return len({Matrix([p[i:i+n] for i in range(n)]).per() for p in permutations(range(1,n<<1))}) # Chai Wah Wu, Feb 12 2024

Extensions

a(6) from Michel Marcus, Feb 08 2024