The rooted Fibonacci trees Tn are defined recursively in the following way. T1 and T2 are both the rooted tree consisting of a single vertex, and for n = 3, 4, ...., the rooted tree Tn is constructed from a root with Tn-1 as its left subtree and Tn-2 as its right subtree.
Draw the first seven rooted Fibonacci trees.
How many vertices, leaves, and internal vertices does the rooted Fibonacci tree Tn have, where n is a positive integer? What is its height?