Rhombus Tilings
Problem 594
For a polygon , let be the number of ways in which can be tiled using rhombi and squares with edge length 1. Distinct rotations and reflections are counted as separate tilings.
For example, if is a regular octagon with edge length 1, then . As it happens, all these 8 tilings are rotations of one another:
Let be the equal-angled convex octagon whose edges alternate in length between and .
For example, here is , with one of its tilings:
For example, here is , with one of its tilings:
You are given that , and .
Find .