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%I #23 Sep 16 2023 06:50:45
%S 0,19,4629,7171257,89765448427
%N Number of matrices with multiple eigenvalues from the set of n X n matrices with elements {-1, 0, +1}.
%D 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.
%H Robert Corless and Steven Thornton, <a href="http://www.bohemianmatrices.com/assets/images/posters/The_Bohemian_Eigenvalue_Project-FIRS_2017.pdf">The Bohemian Eigenvalue Project</a>, 2017 poster.
%H <a href="https://github.com/steventhornton/BHIME-Project">GitHub repository for code used to generate this sequence.</a>
%F a(n) <= A060722(n) where A060722(n) = 3^(n^2); see Corless and Thornton poster link. _Robert P. P. McKone_, Sep 16 2023
%t 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 *)
%Y Number of characteristic polynomials A272658.
%Y Cf. A060722.
%K nonn,more,hard
%O 1,2
%A _Steven E. Thornton_, Jul 13 2016
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