cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A272658 Number of distinct characteristic polynomials of n X n matrices with elements {-1, 0, +1}.

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%I A272658 #53 Sep 30 2023 18:30:07
%S A272658 1,3,16,209,8739,1839102
%N A272658 Number of distinct characteristic polynomials of n X n matrices with elements {-1, 0, +1}.
%D A272658 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.)
%H A272658 Eunice Y. S. Chan, <a href="https://ir.lib.uwo.ca/etd/6414">Algebraic Companions and Linearizations</a>, The University of Western Ontario (Canada, 2019) Electronic Thesis and Dissertation Repository. 6414.
%H A272658 Eunice Y. S. Chan and Robert Corless, <a href="https://doi.org/10.13001/1081-3810.3400">A new kind of companion matrix</a>, Electronic Journal of Linear Algebra, Volume 32, Article 25, 2017, see p. 335.
%H A272658 Robert M. Corless et al., <a href="https://web.archive.org/web/20230228075456/https://s3.amazonaws.com/stevenethornton.github/BHIME+Slides.pdf">Bohemian Eigenvalues</a>.
%H A272658 Robert Corless and Steven Thornton, <a href="http://www.bohemianmatrices.com/assets/images/posters/The_Bohemian_Eigenvalue_Project-FIRS_2017.pdf">The Bohemian Eigenvalue Project</a>, 2017 poster.
%F A272658 a(n) <= 3^(n^2). - _Robert P. P. McKone_, Sep 16 2023
%t A272658 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 *)
%o A272658 (Python)
%o A272658 from itertools import product
%o A272658 from sympy import Matrix
%o A272658 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
%Y A272658 Six classes of matrices mentioned in Rob Corless's talk: this sequence, A272659, A272660, A272661, A272662, A272663.
%Y A272658 Other properties of this class of matrices: A271570, A271587, A271588. - _Steven E. Thornton_, Jul 13 2016
%K A272658 nonn,more,hard
%O A272658 0,2
%A A272658 _N. J. A. Sloane_, May 15 2016
%E A272658 a(4) found by Daniel Lichtblau, May 13 2016
%E A272658 a(5) found by Daniel Lichtblau and _Steven E. Thornton_, May 19 2016
%E A272658 a(0)=1 prepended by _Alois P. Heinz_, Sep 28 2023