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

3, 21, 375, 24823

Offset

1,1

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

Table of n, a(n) for n=1..4.

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.

Formula

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

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 *)

Crossrefs

Number of characteristic polynomials: A272658.

Cf. A060722.

Sequence in context: A353321 A108716 A358950 * A084620 A120603 A336578

Adjacent sequences: A271567 A271568 A271569 * A271571 A271572 A271573

Keyword

nonn,more,hard

Author

Steven E. Thornton, Jul 13 2016

Status

approved