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

0,1

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

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

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

Formula

G.f. = x^21/(x^22 + x + 1), over GF(2). - M. F. Hasler, Feb 17 2018

Prog

(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

Crossrefs

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

Sequence in context: A011737 A011736 A085982 * A355816 A353483 A353809

Adjacent sequences: A011732 A011733 A011734 * A011736 A011737 A011738

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Feb 17 2018

Status

approved