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A272658 Number of distinct characteristic polynomials of n X n matrices with elements {-1, 0, +1}. 14
1, 3, 16, 209, 8739, 1839102 (list; graph; refs; listen; history; text; internal format)
Robert M. Corless, Bohemian Eigenvalues, Talk Presented at Computational Discovery in Mathematics (ACMES 2), University of Western Ontario, May 12 2016. (Talk based on joint work with Steven E. Thornton, Sonia Gupta, Jonathan Brino-Tarasoff, Venkat Balasubramanian.)
Eunice Y. S. Chan, Algebraic Companions and Linearizations, The University of Western Ontario (Canada, 2019) Electronic Thesis and Dissertation Repository. 6414.
Eunice Y. S. Chan and Robert Corless, A new kind of companion matrix, Electronic Journal of Linear Algebra, Volume 32, Article 25, 2017, see p. 335.
Robert M. Corless et al., Bohemian Eigenvalues.
Robert Corless and Steven Thornton, The Bohemian Eigenvalue Project, 2017 poster.
a(n) <= 3^(n^2). - Robert P. P. McKone, Sep 16 2023
a[n_] := a[n] = Module[{m, cPolys}, m = Tuples[Tuples[{-1, 0, 1}, n], n]; cPolys = CharacteristicPolynomial[#, x] & /@ m; Length[DeleteDuplicates[cPolys]]]; Table[a[i], {i, 1, 3}] (* Robert P. P. McKone, Sep 16 2023 *)
from itertools import product
from sympy import Matrix
def A272658(n): return len({tuple(Matrix(n, n, p).charpoly().as_list()) for p in product((-1, 0, 1), repeat=n**2)}) if n else 1 # Chai Wah Wu, Sep 30 2023
Six classes of matrices mentioned in Rob Corless's talk: this sequence, A272659, A272660, A272661, A272662, A272663.
Other properties of this class of matrices: A271570, A271587, A271588. - Steven E. Thornton, Jul 13 2016
Sequence in context: A166860 A196562 A317073 * A326903 A113597 A361366
N. J. A. Sloane, May 15 2016
a(4) found by Daniel Lichtblau, May 13 2016
a(5) found by Daniel Lichtblau and Steven E. Thornton, May 19 2016
a(0)=1 prepended by Alois P. Heinz, Sep 28 2023

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Last modified December 9 15:36 EST 2023. Contains 367693 sequences. (Running on oeis4.)