Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. For example, a(4) = 5 because:

Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1.

(i)	Calculate a(n) and b(n) for n 8. What do you notice about these sequences?
(ii)	Find a relation between a(p) and b(q).
(iii)	Prove your conjectures.