A011686 A binary m-sequence: expansion of reciprocal of x^7 + x^6 + 1.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1

Offset

0,1

Comments

Sequence is 127-periodic. - Ray Chandler, Jun 24 2017

References

S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.

H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Links

Joris Van Kerrebrouck, Table of n, a(n) for n = 0..126

Index entries for linear recurrences with constant coefficients, order 127.

Formula

a(n) = a(n+127). - Gheorghe Coserea, Jun 15 2017

Prog

(MATLAB)
Feedback_shiftregister =[1, 1, 0, 0, 0, 0, 0];    % x^7 + x^6 (+1)
sequence = [0 0 0 0 0 0 1];                 % start sequence
for i = 1:127-7
    sequence(i+7)=mod(Feedback_shiftregister*sequence(i:i+6)', 2)
end % Joris Van Kerrebrouck, Jun 13 2017

Crossrefs

Sequence in context: A079365 A037822 A144600 * A275305 A169671 A070108

Adjacent sequences: A011683 A011684 A011685 * A011687 A011688 A011689

Keyword

nonn

Author

N. J. A. Sloane

Status

approved