RU-ALLRUSSIAN 1963 Problem 13

We place labeled points on a circle as follows. At step 1, take two points at opposite ends of a diameter and label them both 1. At step $\mathrm{n} > 1$ , place a point at the midpoint of each arc created at step $\mathrm{n} - 1$ and label it with the sum of the labels at the two adjacent points. What is the total sum of the labels after step $\mathrm{n}$ ?

For example, after step 4 we have: 1, 4, 3, 5, 2, 5, 3, 4, 1, 4, 3, 5, 2, 5, 4, 3, 4.