A011735 A binary m-sequence: expansion of reciprocal of x^22 + x + 1 (mod 2, shifted by 21 initial 0's).

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Sequence is 2^22-1 = 4194303-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

• Index entries for linear recurrences with constant coefficients, order 4194303.

Crossrefs

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

Programs

PARI

A=matrix(N=22,N, i, j, if(i>1, i==j+1, setsearch([1,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^21/(x^22 + x + 1), over GF(2). - M. F. Hasler, Feb 17 2018

Extensions

Edited by M. F. Hasler, Feb 17 2018