A011743 A binary m-sequence: expansion of reciprocal of x^30 + x^16 + x^15 + x + 1 (mod 2, shifted by 29 initial 0's).

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

Offset

0,1

Comments

Periodic with length of period 2^30-1. - M. F. Hasler, Feb 17 2018

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

Table of n, a(n) for n=0..80.

Prog

(PARI) A011743_vec=concat([1..29]*0, Vec(1/(x^30+x^16+x^15+x+1)+O(x^99))%2)
A=matrix(30, 30, i, j, if(i>1, i==j+1, setsearch([1, 15, 16, 30], j)>0))*Mod(1, 2);
A011743(n)=lift((A^(n-29))[1, 1]) \\ M. F. Hasler, Feb 17 2018

Crossrefs

Cf. A011655, A011656, ..., A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Sequence in context: A354996 A351539 A354926 * A011742 A011741 A369058

Adjacent sequences: A011740 A011741 A011742 * A011744 A011745 A011746

Keyword

nonn

Author

N. J. A. Sloane

Status

approved