Towers Of Hanoi

In the Towers of Hanoi puzzle, you can only move one disk at a time and you can’t put a larger disk on a smaller one.  How many moves does it take to move the stack of 3 to a different peg?

You can break it down like this: first, move the green stack to another peg (3 moves). Then, move the yellow disk (1 move). Finally, move the green stack again (3 moves). In total, it takes 3+1+3=7 moves. 

Can you use recursive thinking to figure out how many moves it would take for a stack of four?

How about a stack of 64?