EDX is offering for time been an really interesting course (Louv1.01x Paradigms of Computer Programming) about the theory of computer programming. One of the homework was to use tail recursion in order to calculate the Fibonacci sequence. Because the solution is really smart I like to put some Python code to show the concept.

From the mathematical point of view you can see the Fibonacci sequence some think like:

a, b, a+b, a+2b, 2a+3b, 3a+5b, 5a + 8b, 8a +13b

0, 1, 1, 2, 3, 5, 8, 13,

so in general: F(a, b, n) = F(b, a+b, n-1) 

this can generate the following code:

def fibonacci_calc(acc1=0, acc2=1, nummber = 0):
if nummber == 0:
return acc1
elif nummber == 1:
return acc2
return fibonacci_calc(acc2, acc2+acc1, nummber-1)

and the hole code can be called like:
fibonacci_calc(0, 1, n)
I wish you happy coding…