Q: Does the recursive version usually use less memory?
  A: No -- it usually uses more memory (for the stack).

  Q: Then why use recursion??
  A: Sometimes it is much simpler to write the recursive version (but

factorial(n) = if n = 0 then 1 else n * factorial(n - 1)

factorial(n) = f_iter(n, 1)

f_iter(n, a) = if n = 0 then a else f_iter(n - 1, n * a)

a = 1;
while (n != 0) {
    a = n * a;
    n = n - 1;
}
return a;

#recursive version
def fib(n):
     if n==0 or n==1:
             return n
     else:
             return fib(n-1)+fib(n-2)

#iterative version
def fib2(n):
     if n==0 or n==1:
             return n
     prev1,prev2=0,1 # start from the base case
     for i in xrange(n):
             cur=prev1+prev2 #build the solution for the next case using the previous solutions
             prev1,prev2=cur,prev1
     return cur

f (n) = n if n<3
f (n) = f (n - 1) + 2f (n - 2) + 3f (n - 3) if n>= 3