# Problem 594: Rhombus Tilings
For a polygon \$P\$, let \$t(P)\$ be the number of ways in which \$P\$
can be tiled using rhombi and squares with edge length 1. Distinct
rotations and reflections are counted as separate tilings. For example,
if \$O\$ is a regular octagon with edge length 1, then \$t(O) = 8\$. As
it happens, all these 8 tilings are rotations of one another: Let
\$O\_{a,b}\$ be the equal-angled convex octagon whose edges alternate in
length between \$a\$ and \$b\$. For example, here is \$O\_{2,1}\$, with
one of its tilings: You are given that \$t(O\_{1,1})=8\$,
\$t(O\_{2,1})=76\$ and \$t(O\_{3,2})=456572\$. Find \$t(O\_{4,2})\$.