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A098532 Sum of sixth powers of first n Fibonacci numbers. 9
0, 1, 2, 66, 795, 16420, 278564, 5105373, 90871494, 1635675910, 29316316535, 526297607496, 9442398055752, 169448124595321, 3040546683808010, 54560921044808010, 979052407236876819, 17568407254504944748 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 06:35 EST 2022. Contains 358582 sequences. (Running on oeis4.)