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

1,2

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

Table of n, a(n) for n=1..5.

Robert Corless and Steven Thornton, The Bohemian Eigenvalue Project, 2017 poster.

GitHub repository for code used to generate this sequence.

Formula

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

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 *)

Crossrefs

Number of characteristic polynomials A272658.

Cf. A060722.

Sequence in context: A281820 A213450 A099809 * A233464 A145214 A172662

Adjacent sequences: A271585 A271586 A271587 * A271589 A271590 A271591

Keyword

nonn,more,hard

Author

Steven E. Thornton, Jul 13 2016

Status

approved