Consider the following problem:
3 1x1 tiles (T1, T2, and T3) - let's call them blue, red, yellow - are used to tile a 1xN walkway. The question is: How many possible ways are there to construct a walkway N units long while ensuring that there are no blue tiles next to each other?
Obviously the question is trivial without the final condition, but with it included it becomes much harder. Looking for a) both an open and closed-form formula for walkway N, and b) a generalization of the problem if possible. I'm interested to see how the problem behaves for NxN walkways, different conditions and Nx1/1xN/NxN tiles.
Preemptively: Not a duplicate of Tile a 1 x n walkway with 4 different types of tiles... - this question considers exclusion, extending its bounds.