Discrete Mathematics An Open Introduction, 4th Edition

What is the smallest number of moves required to transport 2 disks to another pillar?

What is the smallest number of moves required to transport 3 disks to another pillar?

What is the smallest number of moves required to transport 4 disks to another pillar?

Therefore, the smallest number of moves required to move five disks is:

Generalize the last observation. Let $a_n$ represent the smallest number of moves required to transport $n$ disks from the start pillar to another pillar. Then $a_{n-1}$ represents the number of moves required to transport $n-1$ disks to another pillar.

Give a formula for $a_n$ in terms of $a_{n-1}\text{.}$

$a_n=$.