A271570 Number of distinct eigenvalues of n X n matrices with elements {-1, 0, +1}.

3, 21, 375, 24823

Offset: 1

Author

Steven E. Thornton, Jul 13 2016

Keywords

• nonn
• more
• hard

References

• 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.

Links

• Robert Corless and Steven Thornton, The Bohemian Eigenvalue Project, 2017 poster.
• Steven E. Thornton, GitHub repository for code used to generate this sequence.
• Steven E. Thornton & Robert M. Corless, The Bohemian Eigenvalue Project.

Crossrefs

Number of characteristic polynomials: A272658.

Cf. A060722.

Programs

Mathematica

(* Program not suitable to compute more than 3 terms *)
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];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 3}] (* Jean-François Alcover, Jun 17 2018 *)

Formula

a(n) <= 3^(n^2). - Robert P. P. McKone, Sep 16 2023