%I #29 Feb 22 2018 16:33:22
%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,
%T 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,
%U 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
%N A binary m-sequence: expansion of reciprocal of x^3 + x^2 + 1 (mod 2), shifted by 2 initial 0's.
%C Period 7.
%D S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1).
%F G.f.: (x^6 + x^5 + x^4 + x^2)/(1-x^7). a(n+7) = a(n). - _Ralf Stephan_, Aug 05 2013
%F G.f.: x^2/(1 + x^2 + x^3) in GF(2). - _M. F. Hasler_, Feb 16 2018
%t PadLeft[ Mod[ CoefficientList[ Series[1/(1 + x^2 + x^3), {x, 0, 102}], x], 2], 105] (* _Robert G. Wilson v_ *)
%o (PARI) A011656_vec(N)=concat([0,0],Vec(lift(O(x^(N-1))+Mod(1,2)/(1+x^2+x^3))))
%o A011656(n)=(n%7>3)||(n%7==2) \\ Faster than polcoeff(.../(1+x^2+x^3),n-2). - _M. F. Hasler_, Feb 17 2018
%Y Cf. A077962.
%Y Cf. A011655..A011751 for other binary m-sequences.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_