A271588 Number of matrices with multiple eigenvalues from the set of n X n matrices with elements {-1, 0, +1}.

0, 19, 4629, 7171257, 89765448427

Offset: 1

Author

Steven E. Thornton, Jul 13 2016

Keywords

• nonn
• more
• hard

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

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

Crossrefs

Number of characteristic polynomials A272658.

Cf. A060722.

Programs

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 *)

Formula

a(n) <= A060722(n) where A060722(n) = 3^(n^2); see Corless and Thornton poster link. Robert P. P. McKone, Sep 16 2023