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A098533 Sum of seventh powers of first n Fibonacci numbers. 9
0, 1, 2, 130, 2317, 80442, 2177594, 64926111, 1866014652, 54389364796, 1576824599171, 45808159494700, 1329726624043564, 38611060907763141, 1121015217730946894, 32548443577940946894, 945021540449512861377 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (22,252,-1365,-728,2912,-819,-294,20,1).
FORMULA
a(n) = (1/79750)*( 88*F(7n+1) +198*F(7n+2) -(-1)^n*(1218*F(5n+1) + 812*F(5n+2)) +6699*F(3n+2) -(-1)^n*(44660*F(n+1) -22330*F(n+2)) + 17375) where F(n)=A000045(n).
a(n) = 22 a(n-1) +252 a(n-2) -1365 a(n-3) -728 a(n-4) +2912 a(n-5) -819 a(n-6) -294 a(n-7) +20 a(n-8) +1 a(n-9).
G.f.: x*(x^6+20*x^5-166*x^4-318*x^3+166*x^2+20*x-1)/((x-1)*(x^2-11*x-1)*(x^2-x-1)*(x^2+4*x-1)*(x^2+29*x-1)). - R. J. Mathar, Feb 26 2012
MATHEMATICA
Accumulate[Fibonacci[Range[0, 20]]^7] (* Harvey P. Dale, Jul 16 2017 *)
PROG
(PARI) a(n)=sum(i=0, n, fibonacci(i)^7)
(Magma) [(&+[Fibonacci(k)^7:k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jan 17 2018
CROSSREFS
Sequence in context: A300292 A259109 A190578 * A182421 A218434 A354054
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Sep 12 2004
EXTENSIONS
Typo in data corrected by D. S. McNeil, Aug 17 2010
STATUS
approved

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Last modified May 23 10:34 EDT 2024. Contains 372760 sequences. (Running on oeis4.)