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A098533 Sum of seventh powers of first n Fibonacci numbers. 9

%I

%S 0,1,2,130,2317,80442,2177594,64926111,1866014652,54389364796,

%T 1576824599171,45808159494700,1329726624043564,38611060907763141,

%U 1121015217730946894,32548443577940946894,945021540449512861377

%N Sum of seventh powers of first n Fibonacci numbers.

%H G. C. Greubel, <a href="/A098533/b098533.txt">Table of n, a(n) for n = 0..680</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (22,252,-1365,-728,2912,-819,-294,20,1).

%F 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).

%F 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).

%F 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

%t Accumulate[Fibonacci[Range[0,20]]^7] (* _Harvey P. Dale_, Jul 16 2017 *)

%o (PARI) a(n)=sum(i=0,n,fibonacci(i)^7)

%o (MAGMA) [(&+[Fibonacci(k)^7:k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Jan 17 2018

%Y Cf. A001654, A005968, A005969, A098531, A098532.

%Y Cf. A128696, A000071, A001654, A005968, A005969, A098531, A098532, A128697.

%K nonn,easy

%O 0,3

%A _Benoit Cloitre_, Sep 12 2004

%E Typo in data corrected by _D. S. McNeil_, Aug 17 2010

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Last modified February 20 15:52 EST 2020. Contains 332078 sequences. (Running on oeis4.)