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

0,1

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..104.

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

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A077962.

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

Sequence in context: A324682 A288132 A324903 * A295309 A353670 A252744

Adjacent sequences: A011653 A011654 A011655 * A011657 A011658 A011659

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved