3. A trinary tree is a tree in which each node has between 0 and 3 children (call these the left child, middle child, and right child). Define T(h) for h 1 to be the number of distinct trinary tree structures with height h. We don't care about the contents, just the overall structure. What is T(-1) and why? (b) What is T(0) and why? What is T(1) and why? (d) Prove that for h 1 we have: [5 pts] [5 pts] [5 pts] [20 pts] T(h)=3T(h1)(T(1)+T(0)+...+T(h2))2+3T(h1)2(T(1)+T(0)+...+T(h2))+T(h1)3 (e) Use this to calculate T(2) for n = 2. [5 pts]