

A272658


Number of distinct characteristic polynomials of n X n matrices with elements {1, 0, +1}.


14




OFFSET

0,2


REFERENCES

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 BrinoTarasoff, Venkat Balasubramanian.)


LINKS



FORMULA



MATHEMATICA

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


CROSSREFS



KEYWORD

nonn,more,hard


AUTHOR



EXTENSIONS

a(4) found by Daniel Lichtblau, May 13 2016


STATUS

approved



