%I #12 Mar 27 2021 03:55:26
%S 3,25,1027,193244
%N Number of distinct eigenvalues of n X n matrices with elements {0, 1, 2}.
%H S. E. Thornton, <a href="http://www.bohemianmatrices.com/cpdb/unstructured/unstructured_0_1_2">Properties of the Bohemian family of n x n matrices with population {0, 1, 2}</a>, Characteristic Polynomial Database.
%o (Python)
%o from itertools import product
%o from sympy.matrices import Matrix
%o def a(n):
%o eigset = set()
%o for e in product([0, 1, 2], repeat=n*n):
%o if n > 1 and e[1] > e[n]: continue
%o M = Matrix([list(e[n*r:n*(r+1)]) for r in range(n)])
%o eigset |= set(eig for eig in M.eigenvals().keys())
%o return len(eigset)
%o print([a(n) for n in range(1, 3)]) # _Michael S. Branicky_, Mar 25 2021
%Y Number of characteristic polynomials is in A272659.
%Y Number of minimal polynomials is in A306783.
%K nonn,more,hard
%O 1,1
%A _Steven E. Thornton_, Mar 10 2019