# How many distinct Unruly boards are there?

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?

• It seems that this game is very similar to Takuzu. – Peter Kagey Nov 24 '17 at 18:52