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%I #19 Feb 22 2018 16:33:49
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,
%T 0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0,
%U 1,1,0,1,0,1,1,0,1,0,0,0,0
%N A binary m-sequence: expansion of reciprocal of x^14 + x^12 + x^11 + x + 1 (mod 2, shifted by 13 initial 0's).
%C Sequence is 16383-periodic. - _Ray Chandler_, Dec 10 2016
%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 Ray Chandler, <a href="/A011727/b011727.txt">Table of n, a(n) for n = 0..17000</a>
%H <a href="/index/Rec#order_16383">Index entries for linear recurrences with constant coefficients</a>, order 16383.
%F G.f. = x^13/(x^14 + x^12 + x^11 + x + 1) over GF(2). - _M. F. Hasler_, Feb 17 2018
%t Mod[#, 2] & /@ CoefficientList[Series[x^13/(x^14 + x^12 + x^11 + x + 1), {x, 0, 105}], x] (* _Michael De Vlieger_, Feb 21 2018 *)
%o (PARI) A011727_vec(N)=Vec(lift(Mod(1,2)/(x^14+x^12+x^11+x+1)+O(x^(N-13))),-N) \\ _M. F. Hasler_, Feb 17 2018
%Y Cf. A011655..A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).
%K nonn
%O 0,1
%A _N. J. A. Sloane_
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