There is a famous puzzle called the Towers of Hanoi that consists of three pegs and n circular disks, all of different sizes. The disks start on the leftmost peg, with the largest disk on the bottom, the second largest on top of it, and so on, up to the smallest disk on top. The goal is to move the disks so that they are stacked in this same order on the rightmost peg. However, you are allowed to move only one disk at a time, and you are never able to place a larger disk on top of a smaller disk. Let tn denote the fewest moves (a move being taking a disk from one peg and placing it onto another) in which you can accomplish the goal. Determine an explicit formula for tn.