The rooted Fibonacci trees T n are defined recursively in the following way. T 1 and T 2 are both the rooted trees consisting of a single vertex, and for n = 3, 4, …, the rooted tree T n is...

Therooted Fibonacci trees T
n are defined recursively in the following way.T1 andT2 are both the rooted trees consisting of a single vertex, and forn = 3, 4, …, the rooted treeT
n is constructed from a root withT
n-1 as its left subtree andT
n-2 as its right subtree.

1. How many vertices, leaves, and internal vertices does the rooted Fibonacci treeT
n have, wheren is a positive integer?

2. What is its height?