A011742 A binary m-sequence: expansion of reciprocal of x^29 + x^2 + 1 (mod 2, shifted by 28 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, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1

Offset

0,1

Comments

Periodic with period of length 2^29 - 1 = 536870911. - 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.

Mathematica

Join[PadRight[{}, 28, 0], Mod[CoefficientList[Series[1/(x^29+x^2+1), {x, 0, 100}], x], 2]] (* Harvey P. Dale, Sep 27 2024 *)

Prog

(PARI) A=matrix(29, 29, i, j, if(i>1, i==j+1, setsearch([2, 29], j)>0))*Mod(1, 2); a(n)=lift((A^(n-28))[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: A351539 A354926 A011743 * A011741 A369058 A277165

Adjacent sequences: A011739 A011740 A011741 * A011743 A011744 A011745

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Feb 17 2018

Status

approved