Robert M. Corless, Bohemian Eigenvalues, Talk Presented at Computational Discovery in Mathematics (ACMES 2), University of Western Ontario, May 12 2016. (Talk based on joint work with Steven E. Thornton, Sonia Gupta, Jonathan Brino-Tarasoff, Venkat Balasubramanian.)
Eunice Y. S. Chan, Algebraic Companions and Linearizations, The University of Western Ontario (Canada, 2019) Electronic Thesis and Dissertation Repository. 6414.
Eunice Y. S. Chan and Robert Corless, A new kind of companion matrix, Electronic Journal of Linear Algebra, Volume 32, Article 25, 2017, see p. 335.
a[n_] := a[n] = Module[{m, cPolys}, m = Tuples[Tuples[{-1, 0, 1}, n], n]; cPolys = CharacteristicPolynomial[#, x] & /@ m; Length[DeleteDuplicates[cPolys]]]; Table[a[i], {i, 1, 3}] (* Robert P. P. McKone, Sep 16 2023 *)
PROG
(Python)
from itertools import product
from sympy import Matrix
def A272658(n): return len({tuple(Matrix(n, n, p).charpoly().as_list()) for p in product((-1, 0, 1), repeat=n**2)}) if n else 1 # Chai Wah Wu, Sep 30 2023
