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%I #27 Sep 16 2023 12:02:31
%S 3,21,375,24823
%N Number of distinct eigenvalues of n X n matrices with elements {-1, 0, +1}.
%D Steven E. Thornton & 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 Steven E. Thornton, <a href="https://github.com/steventhornton/BHIME-Project">GitHub repository for code used to generate this sequence</a>.
%H Steven E. Thornton & Robert M. Corless, <a href="http://www.bohemianeigenvalues.com/">The Bohemian Eigenvalue Project</a>.
%F a(n) <= 3^(n^2). - _Robert P. P. McKone_, Sep 16 2023
%t (* Program not suitable to compute more than 3 terms *)
%t a[n_] := Module[{r, iter}, iter = Table[{r[k], {-1, 0, 1}}, {k, 1, n^2}]; Eigenvalues /@ (Table[Table[(r[# + j]& /@ Range[n]), {j, 0, n^2 - n, n}], Sequence @@ iter // Evaluate] // Flatten[#, n^2 - 1]&) // Flatten // Union // Length];
%t Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 3}] (* _Jean-François Alcover_, Jun 17 2018 *)
%Y Number of characteristic polynomials: A272658.
%Y Cf. A060722.
%K nonn,more,hard
%O 1,1
%A _Steven E. Thornton_, Jul 13 2016
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