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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 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
Robert Corless and Steven Thornton, The Bohemian Eigenvalue Project, 2017 poster.
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

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Last modified April 24 20:08 EDT 2024. Contains 371963 sequences. (Running on oeis4.)