

A272661


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


10




OFFSET

1,1


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 BrinoTarasoff, Venkat Balasubramanian.)


LINKS

Table of n, a(n) for n=1..6.
Robert M. Corless, Steven E. Thornton, Sonia Gupta, Jonathan BrinoTarasoff, Venkat Balasubramanian, Slides from "Bohemian Eigenvalues" talk.
Robert Israel, Examples for n=5


PROG

(MATLAB)
function count = A272661(N)
C = zeros(0, N);
count = 0;
V = zeros(1, N);
L = floor(N/2) + [0:N1];
for x = 0:2^(N^2)1;
r = dec2bin(x+2^(N^2))'0';
A = reshape(r(2:end), N, N);
rowcounts = sum(A, 2);
colcounts = sum(A, 1);
if ~issorted(rowcounts) rowcounts(N) < max(colcounts)
continue
end
for i = 1:N
V(i) = round(det(A  L(i)*eye(N)));
end
if ~ismember(V, C, 'rows')
count = count+1;
C(count, :) = V;
end
end
end % Robert Israel, Aug 18 2016


CROSSREFS

Six classes of matrices mentioned in Rob Corless's talk: A272658, A272659, A272660, A272661, A272662, A272663.
Sequence in context: A005736 A123903 A172401 * A005742 A055612 A236691
Adjacent sequences: A272658 A272659 A272660 * A272662 A272663 A272664


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane, May 15 2016


EXTENSIONS

a(5) from Robert Israel, Aug 18 2016
a(6) from Steven E. Thornton, Mar 09 2019


STATUS

approved



