OFFSET
0,3
COMMENTS
Prime p divides a((p-1)/2) for p = {29,89,101,181,229,...} = A047650[n]. Primes for which golden mean tau is a quadratic residue or Primes of the form x^2 + 20y^2. - Alexander Adamchuk, Aug 07 2006
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (9,32,-100,20,48,-7,-1).
FORMULA
a(n) = -7/22 + 2*F(n+2)/5 + (F(5*(n+1)) + F(5*n))/(5*55) - (-1)^n*(F(3*(n+1)) - F(3*n))/(2*10), where F=A000045. One may use F(5*(n+1)) + F(5*n) = F(5*n+1) + 4*F(5*n+2) (due to the Binet-de Moivre formula).
G.f.: x*(1-7*x-16*x^2+7*x^3+x^4)/((1-x)*(1+4*x-x^2)*(1-x-x^2)*(1-11*x-x^2)). - Bruno Berselli, Oct 12 2012
MATHEMATICA
Accumulate[Fibonacci[Range[0, 20]]^5] (* Harvey P. Dale, Jan 14 2011 *)
CoefficientList[Series[x*(1-7*x-16*x^2+7*x^3+x^4)/((1-x)*(1+4*x-x^2)*(1-x-x^2)*(1-11*x-x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 13 2012 *)
PROG
(PARI) a(n)=sum(i=0, n, fibonacci(i)^5)
(Magma) [(&+[Fibonacci(k)^5:k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jan 17 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Sep 12 2004
EXTENSIONS
Formula corrected, with the author's consent, by Wolfdieter Lang, Oct 12 2012
STATUS
approved