OFFSET
1,2
COMMENTS
Sequence is interesting because of the values of a(n) - a(n-1) that are 12 or 6 for n > 3.
a(2) = 2 is the only even term.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
From Colin Barker, Oct 20 2015: (Start)
a(n) = a(n-1)+a(n-3)-a(n-4) for n>6.
G.f.: x*(x^5+5*x^4+11*x^3+11*x^2+x+1) / ((x-1)^2*(x^2+x+1)).
(End)
EXAMPLE
a(1) = 1 because 1^5 mod 1 = 0.
a(2) = 2 because (1^5 + 1^5) mod (1 + 1) = 0.
MATHEMATICA
lim = 560; s = Accumulate[Fibonacci[Range@lim]^5]; t = Fibonacci@ Range[2 lim] - 1; Select[Range@ lim, Divisible[s[[#]], t[[# + 2]]] &] (* Michael De Vlieger, Nov 19 2015, after Harvey P. Dale at A098531 and A000071 *)
PROG
(PARI) for(n=1, 1e3, if(sum(k=1, n, fibonacci(k)^5) % sum(k=1, n, fibonacci(k)) == 0, print1(n", ")));
(PARI) Vec(x*(x^5+5*x^4+11*x^3+11*x^2+x+1)/((x-1)^2*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Oct 20 2015
(Magma) I:=[1, 2, 13, 25, 31, 43]; [n le 6 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..60]]; // Vincenzo Librandi, Nov 20 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Oct 20 2015
STATUS
approved