cp's OEIS Frontend

A272661 Number of distinct characteristic polynomials of n X n matrices with elements {0, 1}.

%I A272661 #28 Sep 30 2023 18:19:39
%S A272661 1,2,6,32,333,8927,758878
%N A272661 Number of distinct characteristic polynomials of n X n matrices with elements {0, 1}.
%D A272661 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 A272661 Robert M. Corless, Steven E. Thornton, Sonia Gupta, Jonathan Brino-Tarasoff, Venkat Balasubramanian, <a href="https://s3.amazonaws.com/stevenethornton.github/BHIME+Slides.pdf">Slides from "Bohemian Eigenvalues" talk</a>.
%H A272661 Robert Israel, <a href="/A272661/a272661.txt">Examples for n=5</a>
%o A272661 (MATLAB)
%o A272661 function count = A272661(N)
%o A272661   C = zeros(0,N);
%o A272661   count = 0;
%o A272661   V = zeros(1,N);
%o A272661   L = -floor(N/2) + [0:N-1];
%o A272661   for x = 0:2^(N^2)-1;
%o A272661     r = dec2bin(x+2^(N^2))-'0';
%o A272661     A = reshape(r(2:end),N,N);
%o A272661     rowcounts = sum(A,2);
%o A272661     colcounts = sum(A,1);
%o A272661     if ~issorted(rowcounts)|| rowcounts(N) < max(colcounts)
%o A272661       continue
%o A272661     end
%o A272661     for i = 1:N
%o A272661         V(i) = round(det(A - L(i)*eye(N)));
%o A272661     end
%o A272661     if ~ismember(V, C, 'rows')
%o A272661       count = count+1;
%o A272661       C(count,:) = V;
%o A272661     end
%o A272661   end
%o A272661 end  % _Robert Israel_, Aug 18 2016
%o A272661 (Python)
%o A272661 from itertools import product
%o A272661 from sympy import Matrix
%o A272661 def A272661(n): return len({tuple(Matrix(n,n,p).charpoly().as_list()) for p in product((0,1),repeat=n**2)}) if n else 1 # _Chai Wah Wu_, Sep 30 2023
%Y A272661 Six classes of matrices mentioned in Rob Corless's talk: A272658, A272659, A272660, A272661, A272662, A272663.
%K A272661 nonn,more
%O A272661 0,2
%A A272661 _N. J. A. Sloane_, May 15 2016
%E A272661 a(5) from _Robert Israel_, Aug 18 2016
%E A272661 a(6) from _Steven E. Thornton_, Mar 09 2019
%E A272661 a(0)=1 prepended by _Alois P. Heinz_, Sep 28 2023