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A272661 Number of distinct characteristic polynomials of n X n matrices with elements {0, 1}. 10
2, 6, 32, 333, 8927, 758878 (list; graph; refs; listen; history; text; internal format)
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 Brino-Tarasoff, Venkat Balasubramanian.)

LINKS

Table of n, a(n) for n=1..6.

Robert M. Corless, Steven E. Thornton, Sonia Gupta, Jonathan Brino-Tarasoff, 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:N-1];

  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

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Last modified January 19 17:59 EST 2020. Contains 331051 sequences. (Running on oeis4.)