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

1, 1, 6, 513

Offset

0,3

Comments

a(4) >= 308696.

Links

Table of n, a(n) for n=0..3.

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

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}]

Prog

(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

Crossrefs

Cf. A272661, A272659.

Cf. A272658, A272660, A272662, A272663.

Sequence in context: A223050 A290937 A364482 * A250391 A003395 A222607

Adjacent sequences: A365923 A365924 A365925 * A365927 A365928 A365929

Keyword

nonn,hard,more,bref

Author

Robert P. P. McKone, Sep 23 2023

Status

approved