OFFSET
1,2
COMMENTS
a(n) > Fibonacci(n) for n > 1.
{a(n)} = {F(2*n)} union {2} minus {0,3} where F(2*n) = A001906(n) = bisection of Fibonacci sequence.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-1).
FORMULA
From Colin Barker, Jul 29 2014: (Start)
a(n) = 3*a(n-1) - a(n-2) for n>4.
G.f.: -x*(x^3 - 3*x^2 + x - 1) / (x^2 - 3*x + 1). (End)
a(n) = (((3 + sqrt(5))/2)^n - ((3 - sqrt(5))/2)^n)/sqrt(5) for n > 2. - Stefano Spezia, Apr 15 2022
EXAMPLE
377 is the first Fibonacci number that is divisible by 13, the 7th Fibonacci number, so a(7) = 377.
MAPLE
A237268 := proc(n)
coeftayl((1-x+3*x^2-x^3)/(x^2-3*x+1), x=0, n);
end proc:
seq(A237268(n), n=0..30); # Wesley Ivan Hurt, Aug 02 2014
MATHEMATICA
Table[k=1; While[Mod[Fibonacci[k], Fibonacci[n]]!=0||Fibonacci[k]==Fibonacci[n], k++]; Fibonacci[k], {n, 1, 30}]
CoefficientList[Series[-(x^3 - 3 x^2 + x - 1)/(x^2 - 3 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 01 2014 *)
PROG
(PARI) Vec(-x*(x^3-3*x^2+x-1)/(x^2-3*x+1) + O(x^100)) \\ Colin Barker, Jul 29 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michel Lagneau, Feb 05 2014
STATUS
approved