Hanoi of mobile number calculation

A plate is moved 1 times: two plates are three times:

See three more plates:

First move the top two plates to the transition location, which is the C position, which takes three times. Then move the bottom plate to the target position B position, need once, and then move the C-position plate to B position, this time also need three times (oneself can draw). So the operation of three plates can be separated from the problem, that is, the bottom of the plate and the plate above it, and the number of plates on it is two, so this part is back to the problem of handling two plates, but this part we need to operate two times, so it is 2*3, coupled with the bottom of the plate to the target location, At this time need to operate once, so the total is 2*3+1;

Four plates are also so reasoning.

You can finally get a sequence called a (n) =2a (n-1) +1

Hanoi of mobile number calculation