A098532 Sum of sixth powers of first n Fibonacci numbers.

0, 1, 2, 66, 795, 16420, 278564, 5105373, 90871494, 1635675910, 29316316535, 526297607496, 9442398055752, 169448124595321, 3040546683808010, 54560921044808010, 979052407236876819, 17568407254504944748

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..795

Index entries for linear recurrences with constant coefficients, signature(13,104,-260,-260,104,13,-1).

Formula

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).

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

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

a(n)= (F(n)^5 * F(n+3) + F(2*n))/4. - Gary Detlefs, Jan 05 2013

Mathematica

Table[(Fibonacci[n]^5*Fibonacci[n+3] + Fibonacci[2*n])/4, {n, 0, 30}] (* G. C. Greubel, Jan 17 2018 *)

Prog

(PARI) a(n)=sum(i=0, n, fibonacci(i)^6);
(PARI) for(n=0, 30, print1((fibonacci(n)^5*fibonacci(n+3) + fibonacci(2*n))/4, ", ")) \\ G. C. Greubel, Jan 17 2018
(Magma) [(Fibonacci(n)^5*Fibonacci(n+3) + Fibonacci(2*n))/4: n in [0..30]]; // G. C. Greubel, Jan 17 2018

Crossrefs

Cf. A001654, A005968, A005969, A098531, A098533.

Cf. A119287, A000071, A001654, A005968, A005969, A098531, A098533, A128697.

Sequence in context: A226409 A226338 A131472 * A159716 A157060 A154637

Adjacent sequences: A098529 A098530 A098531 * A098533 A098534 A098535

Keyword

nonn,easy

Author

Benoit Cloitre, Sep 12 2004

Status

approved