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A272659 Number of distinct characteristic polynomials of n X n matrices with elements {0, 1, 2}. 15

%I #23 Sep 30 2023 18:29:24

%S 1,3,22,513,58335,40422490

%N Number of distinct characteristic polynomials of n X n matrices with elements {0, 1, 2}.

%H Robert M. Corless, <a href="https://www.youtube.com/watch?v=qB1KZWU8g2U">Bohemian Eigenvalues</a>, 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.)

%o (Python)

%o from itertools import product

%o from sympy import Matrix

%o def A272659(n): return len({tuple(Matrix(n,n,p).charpoly().as_list()) for p in product(range(3),repeat=n**2)}) if n else 1 # _Chai Wah Wu_, Sep 30 2023

%Y Six classes of matrices mentioned in Rob Corless's talk: A272658, A272659, A272660, A272661, A272662, A272663.

%K nonn,more

%O 0,2

%A _N. J. A. Sloane_, May 15 2016

%E a(4) from _Chai Wah Wu_, Dec 03 2018

%E a(5) from _Steven E. Thornton_, Mar 09 2019

%E a(0)=1 prepended by _Alois P. Heinz_, Sep 28 2023

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)