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.
%I A219020 #27 Feb 17 2020 17:46:01
%S A219020 1,7,45,297,2002,13630,93177,638001,4371235,29956465,205313076,
%T A219020 1407206412,9645056785,66107994667,453110391657,3105663400665,
%U A219020 21286529888422,145900036590826,1000013702089545,6854195814790005,46979356835860351,322001301602738017,2207029753248402600,15127206968164865112
%N A219020 Sum of the cubes of the first n even-indexed Fibonacci numbers divided by the sum of the first n terms.
%C A219020 For a Lucas sequence U(k,1), the sum of the cubes of the first n terms is divisible by the sum of the first n terms. This sequence corresponds to the case of k=3.
%H A219020 Vincenzo Librandi, <a href="/A219020/b219020.txt">Table of n, a(n) for n = 1..200</a>
%F A219020 a(n) = Sum_{k=1..n} A001906(k)^3 / Sum_{k=1..n} A001906(k).
%F A219020 a(n) = A163198(n) / A027941(n).
%F A219020 a(n) = 11*a(n-1) - 33*a(n-2) + 33*a(n-3) - 11*a(n-4) + a(n-5). - _Vaclav Kotesovec_, May 23 2013
%F A219020 G.f.: x*(1-4*x+x^2)/((1-x)*(1-7*x+x^2)*(1-3*x+x^2)). [_Bruno Berselli_, Jun 07 2013]
%t A219020 Table[Fibonacci[2*n+1]/4 + LucasL[4*n+2]/20 - 2/5, {n, 1, 20}] (* _Vaclav Kotesovec_, May 23 2013 *)
%t A219020 With[{f=Fibonacci[Range[2,50,2]]},Accumulate[f^3]/Accumulate[f]] (* _Harvey P. Dale_, Feb 17 2020 *)
%o A219020 (PARI) Vec(x*(1-4*x+x^2)/((1-x)*(1-7*x+x^2)*(1-3*x+x^2)) + O(x^100)) \\ _Altug Alkan_, Dec 09 2015
%Y A219020 Cf. A001906, A027941, A163198, A219021.
%K A219020 nonn,easy
%O A219020 1,2
%A A219020 _Max Alekseyev_, Nov 09 2012