The Tower of Hanoi problem:

According to legend, a certain Hindu temple contains three thin diamond poles( , , and is closer to and is closer to but is not closer to ) on one of which, at the time of creation, God placed golden disks that decrease in size as they rise from the base.

The priests of the temple work unceasingly to transfer all the disks one by one from the first pole to one of the others, but they must never place a large disk on top of a smaller one and they are allowed to move disks from one tower to only adjacent pole. Let

Find a recurrence relation and .

Solve for the problem to find (The book did this):

Solve for the problem to find (I did this):

Why my solution of is wrong? For finding I did the same thing as done in finding which is skipping the move from to when moving from to . I calculated this move as like the book did it.

So why am I wrong?

Also my question is why in finding to move the disks from to they skipped to calculate the move to move the disks first from to ?