Problem Solving Exercise

I will be using Polya's method to attempt to solve the problem depicted here.

Understand the Problem

The problem at hand is to predict whether creases on a repeatedly folded paper will be hill or valleys.

Devise a Plan

I will try to fold the paper and record the pattern of hills/valleys after each successive fold, in an attempt to uncover a pattern.

Carry Out the Plan

Folds | Hills | Valleys

   1         0           1

   2         1           3

   3         3           8

   4         8          14

It seems to be the number of valleys is the same as the number of hills for the next fold. I can't figure our another pattern after that thought...

Look Back

I tried one method, perhaps I should try again because I don't see a pattern.

Acknowledge When and How You're Stuck

I don't really see a pattern so I'm quite lost...