#. # The Fibonacci sequence
#.
#. ## Using the closed-form formula as a function
#.
#. When directly executing FeenoX, one gives a single argument to the executable
#. with the path to the main input file.
#. For example, the following input computes the first twenty numbers of the
#. [Fibonacci sequence](https://en.wikipedia.org/wiki/Fibonacci_number) using the closed-form formula
#. 
#. $$
#. f(n) = \frac{\varphi^n - (1-\varphi)^n}{\sqrt{5}}
#. $$
#. 
#. where $\varphi=(1+\sqrt{5})/2$ is the [Golden ratio](https://en.wikipedia.org/wiki/Golden_ratio).
# the fibonacci sequence as function
phi = (1+sqrt(5))/2 
f(n) = (phi^n - (1-phi)^n)/sqrt(5)
PRINT_FUNCTION f MIN 1 MAX 20 STEP 1
#$ $ feenox fibo_formula.fee | tee one
#$ 1	1
#$ 2	1
#$ 3	2
#$ 4	3
#$ 5	5
#$ 6	8
#$ 7	13
#$ 8	21
#$ 9	34
#$ 10	55
#$ 11	89
#$ 12	144
#$ 13	233
#$ 14	377
#$ 15	610
#$ 16	987
#$ 17	1597
#$ 18	2584
#$ 19	4181
#$ 20	6765
#$ $
