Unruly is a puzzle game played on a board of $2n × 2n$ squares. Each square must be colored either black or white, with the following constraints:
- Each column must have $n$ white squares and $n$ black squares.
- Each row must have $n$ white squares and $n$ black squares.
- Nowhere on the board may 3 white squares or 3 black squares appear consecutively, whether horizontally or vertically.
I define two Unruly boards to be equivalent if one can be transformed to the other with any combination of 90° rotations, horizontal flips, vertical flips, or color inversions (i.e., changing all whites to blacks and blacks to whites).
For each $n$, how many non-equivalent Unruly boards are there?