User blog comment:LittlePeng9/Color reducing for Turing machines/@comment-5529393-20130413054452/@comment-1605058-20130413071400

Subscript has length 0 on 1st cell, length 1 on 2nd cell,... length n-1 on nth cell. Now we move left to write states. So we have this 1 with length 0, 2 with length 1, 2^x for any length x. Summing gives 2^n-1.