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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

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

Programs

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 *)

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

Formula

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

Extensions

Edited by M. F. Hasler, Feb 17 2018