# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a219020 Showing 1-1 of 1 %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, Table of n, a(n) for n = 1..200 %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE