Generating functions

• How Many Ways Can You Climb n Stairs Using 2 or 3 at a Time?
  Count ways to climb n stairs using only 2- or 3-stair moves: derive the recurrence, generating function, and an explicit binomial-sum formula.
• How to Find a Closed Form for an nth Term Using Generating Functions
  Turn a recurrence into a generating function, simplify it, and extract its coefficients to obtain a closed form for the nth term.