In this post, we prove the closed form of a nonlinear recurrence corresponding to the count of binary trees with nodes.

# Currently Browsing

## December, 2013

28 December

# Calculating Modified Fibonacci Numbers, Quickly and Exactly

This is inspired by an article of similar name called Calculating Fibonacci Numbers, Quickly and Exactly. Consider the a modified fibonacci sequence given by the recurrence . We shall look at various algebraic and analytic properties of this sequence, find two algorithms that computes in time, and finally look at a motivating example where we need to compute this sequence quickly and exactly.