A011656 A binary m-sequence: expansion of reciprocal of x^3 + x^2 + 1 (mod 2), shifted by 2 initial 0's.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

Crossrefs

Cf. A077962.

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

Programs

Mathematica

PadLeft[ Mod[ CoefficientList[ Series[1/(1 + x^2 + x^3), {x, 0, 102}], x], 2], 105] (* Robert G. Wilson v *)

PARI

A011656_vec(N)=concat([0,0],Vec(lift(O(x^(N-1))+Mod(1,2)/(1+x^2+x^3))))
A011656(n)=(n%7>3)||(n%7==2) \\ Faster than polcoeff(.../(1+x^2+x^3),n-2). - M. F. Hasler, Feb 17 2018

Formula

G.f.: (x^6 + x^5 + x^4 + x^2)/(1-x^7). a(n+7) = a(n). - Ralf Stephan, Aug 05 2013

G.f.: x^2/(1 + x^2 + x^3) in GF(2). - M. F. Hasler, Feb 16 2018