Help interpreting code

[schniefen]

I'm trying to understand the following code that sets up the three term recursion ui+1=a1u1+a0ui-1 as a class:

class Recursion3Term:
    def __init__ (self , a0 , a1 , u0 , u1 ):
        self.coeff = [a1 , a0]
        self.initial = [u1 , u0] 
    def __iter__ ( self ): 
        u1,u0 = self.initial
        yield u0
        yield u1 
        a1,a0=self.coeff
        while True: 
            u1 , u0 = a1*u1 + a0*u0 , u1 
            yield u1 
    def __getitem__ (self,k):
        for i, r in enumerate (self):
            if i == k:
                return r

I would deeply appreciate a short explanation about line 5 to 16. For example in the iterable method, why are the different yield statements necessary? What does the while-loop do? What is r?