A011740 A binary m-sequence: expansion of reciprocal of x^27 + x^8 + x^7 + x + 1 (mod 2, shifted by 26 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1

Offset

0,1

Comments

Sequence is 2^27-1 = 134217727-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 134217727.

Index entries for periodic sequences with large period.

Formula

G.f. = x^26/(x^27 + x^8 + x^7 + x + 1) over GF(2). - M. F. Hasler, Feb 17 2018

Prog

(PARI)  A=matrix(N=27, N, i, j, if(i>1, i==j+1, setsearch([1, 7, 8, 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: A011741 A369058 A277165 * A354344 A085974 A011739

Adjacent sequences: A011737 A011738 A011739 * A011741 A011742 A011743

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Feb 17 2018

Status

approved