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A098532 Sum of sixth powers of first n Fibonacci numbers.

%I A098532 #19 Sep 08 2022 08:45:15
%S A098532 0,1,2,66,795,16420,278564,5105373,90871494,1635675910,29316316535,
%T A098532 526297607496,9442398055752,169448124595321,3040546683808010,
%U A098532 54560921044808010,979052407236876819,17568407254504944748
%N A098532 Sum of sixth powers of first n Fibonacci numbers.
%H A098532 G. C. Greubel, <a href="/A098532/b098532.txt">Table of n, a(n) for n = 0..795</a>
%H A098532 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature(13,104,-260,-260,104,13,-1).
%F A098532 a(n) = (1/500)*(F(6*n+1) +3*F(6*n+2) -(-1)^n*(16*F(4*n+1)+8*F(4*n+2))-60*F(2*n+1) +120*F(2*n+2) -(-1)^n*40 ) where F(n)=A000045(n).
%F A098532 G.f.: x*(1-11*x-64*x^2-11*x^3+x^4)/((x+1)*(1-18*x+x^2)*(1-3*x+x^2)*(1+7*x+x^2)). - _R. J. Mathar_, Feb 26 2012
%F A098532 a(n) = -6*(-1)^n*A049685(n)/125 +3*A002878(n)/25 +A049629(n)/125 -2*(-1)^n/25. - _R. J. Mathar_, Feb 26 2012
%F A098532 a(n)= (F(n)^5 * F(n+3) + F(2*n))/4. - _Gary Detlefs_, Jan 05 2013
%t A098532 Table[(Fibonacci[n]^5*Fibonacci[n+3] + Fibonacci[2*n])/4, {n,0,30}] (* _G. C. Greubel_, Jan 17 2018 *)
%o A098532 (PARI) a(n)=sum(i=0,n,fibonacci(i)^6);
%o A098532 (PARI) for(n=0,30, print1((fibonacci(n)^5*fibonacci(n+3) + fibonacci(2*n))/4, ", ")) \\ _G. C. Greubel_, Jan 17 2018
%o A098532 (Magma) [(Fibonacci(n)^5*Fibonacci(n+3) + Fibonacci(2*n))/4: n in [0..30]]; // _G. C. Greubel_, Jan 17 2018
%Y A098532 Cf. A001654, A005968, A005969, A098531, A098533.
%Y A098532 Cf. A119287, A000071, A001654, A005968, A005969, A098531, A098533, A128697.
%K A098532 nonn,easy
%O A098532 0,3
%A A098532 _Benoit Cloitre_, Sep 12 2004