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