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.

A227047 Expansion of x^2*(1+x^2) / ( (x^2-x+1)*(-x^2-x+1)*(1+x+x^2) ).

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%I A227047 #28 Oct 16 2018 17:54:25
%S A227047 0,0,1,1,2,3,4,7,12,19,31,50,80,130,211,341,552,893,1444,2337,3782,
%T A227047 6119,9901,16020,25920,41940,67861,109801,177662,287463,465124,752587,
%U A227047 1217712,1970299,3188011,5158310,8346320,13504630,21850951,35355581,57206532,92562113,149768644
%N A227047 Expansion of x^2*(1+x^2) / ( (x^2-x+1)*(-x^2-x+1)*(1+x+x^2) ).
%H A227047 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,0,1,1).
%F A227047 a(0)=a(1)=0. a(n+2)=a(n+1)+a(n) + A134667(n+1).
%F A227047 a(2n+1) = A182895(n). a(2n+2) = A182895(n+1)-A182895(n).
%F A227047 a(n+1)/a(n) tends to A001622 (the golden ratio) as n->infinity.
%F A227047 a(n) = A079962(n-2) + A079962(n-4). - _R. J. Mathar_, Jun 30 2013
%F A227047 a(n+6) - a(n-6) = 10*A000045(n).
%F A227047 a(n+3) - a(n-3) = A000032(n).
%F A227047 a(n) = a(n-1) +a(n-3) +a(n-5) +a(n-6). - _Joerg Arndt_, Jun 30 2013
%t A227047 CoefficientList[Series[x^2(1+x^2)/((x^2-x+1)(-x^2-x+1)(1+x+x^2)),{x,0,50}],x] (* or *) LinearRecurrence[{1,0,1,0,1,1},{0,0,1,1,2,3},50] (* _Harvey P. Dale_, Oct 16 2018 *)
%K A227047 nonn,less,easy
%O A227047 0,5
%A A227047 _Paul Curtz_, Jun 29 2013