A306792 Number of distinct eigenvalues of n X n matrices with elements {0, 1, 2}.

3, 25, 1027, 193244

Offset: 1

Author

Steven E. Thornton, Mar 10 2019

Keywords

• nonn
• more
• hard

Links

• S. E. Thornton, Properties of the Bohemian family of n x n matrices with population {0, 1, 2}, Characteristic Polynomial Database.

Crossrefs

Number of characteristic polynomials is in A272659.

Number of minimal polynomials is in A306783.

Programs

Python

from itertools import product
from sympy.matrices import Matrix
def a(n):
  eigset = set()
  for e in product([0, 1, 2], repeat=n*n):
    if n > 1 and e[1] > e[n]: continue
    M = Matrix([list(e[n*r:n*(r+1)]) for r in range(n)])
    eigset |= set(eig for eig in M.eigenvals().keys())
  return len(eigset)
print([a(n) for n in range(1, 3)]) # Michael S. Branicky, Mar 25 2021