Let \mathbb{N}_{0} be the set of non-negative integers. There is a triple (f, a, b), where f is a function from \mathbb{N}_{0} to \mathbb{N}_{0} and a, b \in \mathbb{N}_{0}, that satisfies the following conditions:
(1) f(1)=2.
(2) f(a)+f(b) \leq 2 \sqrt{f(a)}.
(3) For all n>0, we have f(n)=f(n-1) f(b)+2 n-f(b).
Find the sum of all possible values of f(b+100).