How was the recursive fibonacci function derived?

Question

In python, a recursive function for a Fibonacci sequence that returns the nth fibonacci number can be written as:

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

I understand how this function works, but if someone were to have never seen this function before, how would one derive it?

Thanks

Answer 1

It's just a crude translation of the mathematical definition of the Fibonacci sequence.

The Fibonacci sequence is defined as:

F ₀ = 0

F ₁ = 1

F _n = F _n-1 + F _n-2

You can see that the Python code is basically a direct translation of this (except with n off by 1).