How to write the Fibonacci Sequence?

Question

I had originally coded the program wrongly. Instead of returning the Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 should = only those numbers between 1

Answer 1

The idea behind the Fibonacci sequence is shown in the following Python code:

def fib(n):
   if n == 1:
      return 1
   elif n == 0:   
      return 0            
   else:                      
      return fib(n-1) + fib(n-2)         

This means that fib is a function that can do one of three things. It defines fib(1) == 1, fib(0) == 0, and fib(n) to be:

fib(n-1) + fib(n-2)

Where n is an arbitrary integer. This means that fib(2) for example, expands out to the following arithmetic:

fib(2) = fib(1) + fib(0)
fib(1) = 1
fib(0) = 0
# Therefore by substitution:
fib(2) = 1 + 0
fib(2) = 1

We can calculate fib(3) the same way with the arithmetic shown below:

fib(3) = fib(2) + fib(1)
fib(2) = fib(1) + fib(0)
fib(2) = 1
fib(1) = 1
fib(0) = 0
# Therefore by substitution:
fib(3) = 1 + 1 + 0

The important thing to realize here is that fib(3) can't be calculated without calculating fib(2), which is calculated by knowing the definitions of fib(1) and fib(0). Having a function call itself like the fibonacci function does is called recursion, and it's an important topic in programming.

This sounds like a homework assignment so I'm not going to do the start/end part for you. Python is a wonderfully expressive language for this though, so this should make sense if you understand math, and will hopefully teach you about recursion. Good luck!

Edit: One potential criticism of my code is that it doesn't use the super-handy Python function yield, which makes the fib(n) function a lot shorter. My example is a little bit more generic though, since not a lot of languages outside Python actually have yield.