A011657 A binary m-sequence: expansion of reciprocal of x^3 + x + 1 (mod 2, shifted by 2 initial 0's).

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

Offset

0,1

Comments

Period 7.

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, signature (0,0,0,0,0,0,1).

Formula

G.f.: (x^6 + x^3 + x + 1)/(1-x^7), a(n+7) = a(n). - Ralf Stephan, Aug 05 2013

Mathematica

Join[{0, 0}, Mod[CoefficientList[1/(x^3 + x + 1) + O[x]^80, x], 2]] (* Jean-François Alcover, Feb 23 2018 *)

Prog

(PARI) A011657(n)=bittest(92, n%7) \\ M. F. Hasler, Feb 17 2018

Crossrefs

Cf. A011655..A011751 for other binary m-sequences.

Sequence in context: A373470 A373141 A323158 * A354896 A359606 A072126

Adjacent sequences: A011654 A011655 A011656 * A011658 A011659 A011660

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved