If W n is the minimum number of moves needed to transfer a tower of n disks from one peg to another when there are four pegs instead of three, show that (Here T n = 2 n − 1 is the ordinary three-peg...

If W_n
is the minimum number of moves needed to transfer a tower of n disks from one peg to another when there are four pegs instead of three, show that

(Here T_n
= 2ⁿ
− 1 is the ordinary three-peg number.) Use this to find a closed form f(n) such that