A369944 a(n) is the number of distinct values of the determinant of an n X n Hankel matrix using the integers 0 to 2*(n - 1).

1, 1, 3, 44, 1292, 43958, 2204010

Offset: 0

Author

Stefano Spezia, Feb 06 2024

Keywords

• nonn
• hard
• more

Links

• Wikipedia, Hankel matrix.

Crossrefs

Cf. A368353, A368354, A368355.

Programs

Mathematica

a[n_] := CountDistinct[Table[Det[HankelMatrix[Join[Drop[per = Part[Permutations[Range[0, 2 n - 2]], 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=[0..2*n-2], list=List()); forperm(v, p, listput(list, matdet(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 A369944(n): return len({Matrix([p[i:i+n] for i in range(n)]).det() for p in permutations(range((n<<1)-1))}) # Chai Wah Wu, Feb 12 2024

Extensions

a(6) from Michel Marcus, Feb 08 2024