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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)
 OFFSET 0,2 REFERENCES 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.) LINKS Table of n, a(n) for n=0..5. 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. FORMULA a(n) <= 3^(n^2). - Robert P. P. McKone, Sep 16 2023 MATHEMATICA 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 *) PROG (Python) 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 CROSSREFS 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 Adjacent sequences: A272655 A272656 A272657 * A272659 A272660 A272661 KEYWORD nonn,more,hard AUTHOR N. J. A. Sloane, May 15 2016 EXTENSIONS 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 STATUS approved

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