A365926 Number of distinct characteristic polynomials for n X n matrices with entries in {0, 1, ..., n-1}.

1, 1, 6, 513, 2875405

Offset: 0

Author

Robert P. P. McKone, Sep 23 2023

Keywords

• nonn
• hard
• more
• bref

Links

• Robert P. P. McKone, The distinct characteristic polynomials for a(2)-a(3).

Crossrefs

Cf. A272661, A272659.

Cf. A272658, A272660, A272662, A272663.

Programs

Mathematica

a[n_] := Module[{polynomials = {}, polynomial}, Monitor[Do[polynomial = CharacteristicPolynomial[ArrayReshape[IntegerDigits[i, n, n^2], {n, n}], x]; If[Not[MemberQ[polynomials, polynomial]], AppendTo[polynomials, polynomial]];, {i, 0, n^(n^2) - 1}], {n, {i, n^(n^2) - 1}, ProgressIndicator[i, {0, n^(n^2) - 1}]}]; Length[polynomials]]; Table[a[n], {n, 1, 3}]

Python

from itertools import product
from sympy import Matrix
def A365926(n): return len({tuple(Matrix(n,n,p).charpoly().as_list()) for p in product(range(n),repeat=n**2)}) if n else 1 # Chai Wah Wu, Sep 30 2023

Extensions

a(4) from Robin Visser, May 04 2025