cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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