Find a recursive relation for the number of distinct ordered pairs (a,b) of non-negative integers satisfying 2a+5b=100.

Okay, so I took an entirely different approach to this question using generating functions unlike my book. However I am stuck at the end. Any assistance to finish it off would be highly appreciated!

Let be the number of nonnegative ordered pairs which solve .

We define and

Now

Clearly, is the generating function sequence for the sequence

We can see from inspection that and

But up to this step, I have no idea how to get the recursive relation for

Many thanks!