I came across this integer sequence: A133792. It represents the number of $n\times n$ binary matrices with every 1 adjacent to some zero and every 0 adjacent to some one, horizontally or vertically.
Now, assuming there exists a way except for bruteforce, how would I go about to calculate this number? (As enumerating valid matrices one-by-one seems hardly feasible, given the fast growing nature of the sequence.)
For even ns, I think the problem is related to tiling patterns of dominoes on checkerboards (or at least, using two colored dominoes would ensure that the adjacency constraint won't be violated).