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A271588
Number of matrices with multiple eigenvalues from the set of n X n matrices with elements {-1, 0, +1}.
2
0, 19, 4629, 7171257, 89765448427
OFFSET
1,2
REFERENCES
Steven E. Thornton and Robert M. Corless, The Bohemian Eigenvalue Project, Poster Presented at The International Symposium on Symbolic and Algebraic Computation (ISSAC 2016). Wilfrid Laurier University, July 19-22, 2016.
FORMULA
a(n) <= A060722(n) where A060722(n) = 3^(n^2); see Corless and Thornton poster link. Robert P. P. McKone, Sep 16 2023
MATHEMATICA
a[n_Integer?NonNegative] := a[n] = Module[{m, ei}, ei[matrix_] := Length[Select[Tally[Eigenvalues[matrix]], Last[#] > 1 &]] > 0; m = Tuples[Tuples[{-1, 0, 1}, n], n]; Count[m, mat_ /; ei[mat]]]; Table[a[i], {i, 1, 3}] (* Robert P. P. McKone, Sep 16 2023 *)
CROSSREFS
Number of characteristic polynomials A272658.
Cf. A060722.
Sequence in context: A281820 A213450 A099809 * A233464 A145214 A172662
KEYWORD
nonn,more,hard
AUTHOR
Steven E. Thornton, Jul 13 2016
STATUS
approved