A011734 A binary m-sequence: expansion of reciprocal of x^21 + x^2 + 1 (mod 2, shifted by 20 initial 0's).

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

Offset

0,1

Comments

Sequence is 2^21-1 = 2097151-periodic. - 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.

Formula

G.f. = x^20/(x^21 + x^2 + 1), over GF(2). - M. F. Hasler, Feb 17 2018

Mathematica

Join[PadRight[{}, 20, 0], (Mod[#, 2]&/@CoefficientList[Series[1/(x^21+x^2+1), {x, 0, 60}], x])] (* Harvey P. Dale, Jun 01 2020 *)

Prog

(PARI) A=matrix(N=21, N, i, j, if(i>1, i==j+1, setsearch([2, N], j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[1, 1]) \\ M. F. Hasler, Feb 17 2018

Crossrefs

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

Sequence in context: A353482 A336355 A324731 * A276653 A355443 A011733

Adjacent sequences: A011731 A011732 A011733 * A011735 A011736 A011737

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Feb 17 2018

Status

approved