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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 Table of n, a(n) for n=1..5. Robert Corless and Steven Thornton, The Bohemian Eigenvalue Project, 2017 poster. GitHub repository for code used to generate this sequence. 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 Adjacent sequences: A271585 A271586 A271587 * A271589 A271590 A271591 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.)