Fibonacci series recursion error

[rusi]

On May 2, 2:53 pm, Hans Georg Schaathun <h... at schaathun.net> wrote:
> On 02 May 2011 08:56:57 GMT, Steven D'Aprano  <steve+comp.lang.pyt... at pearwood.info> wrote:
>
> :  I see your smiley, but there are a number of similar series as Fibonacci,
> :  with the same recurrence but different starting values, or similar but
> :  slightly different recurrences. E.g. Lucas, primefree, Pell, Padovan and
> :  Perrin numbers.
>
> Well, Fibonacci isn't one unique sequence.  Any sequence satisfying
> f(n) = f(n-1) + f(n-2) is /a/ Fibonacci sequence.  Regardless of
> starting values.  At least according to some authors.

And they all will, when expressed in closed form, be of the form
f(n) = phi^n + something of a smaller order
where phi = (1 + sqrt(5))/2

Since phi > 1 they are exponential, ignoring lower order terms.