A098533 Sum of seventh powers of first n Fibonacci numbers.

0, 1, 2, 130, 2317, 80442, 2177594, 64926111, 1866014652, 54389364796, 1576824599171, 45808159494700, 1329726624043564, 38611060907763141, 1121015217730946894, 32548443577940946894, 945021540449512861377

Offset: 0

Author

Benoit Cloitre, Sep 12 2004

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..680
• Index entries for linear recurrences with constant coefficients, signature (22,252,-1365,-728,2912,-819,-294,20,1).

Crossrefs

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

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

Programs

Magma

[(&+[Fibonacci(k)^7:k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jan 17 2018

Mathematica

Accumulate[Fibonacci[Range[0,20]]^7] (* Harvey P. Dale, Jul 16 2017 *)

PARI

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

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

Extensions

Typo in data corrected by D. S. McNeil, Aug 17 2010