When I saw the recent question Kasteleyn's formula for domino tilings generalized?, I had the idea of generalizing it by introducing an additional variable. I didn't manage to solve the generalized question yet, but working on it, it suddenly occurred to me a couple of days later that the additional variable provided in fact an easy answer of the initial question.

When I saw the recent question Kasteleyn's formula for domino tilings generalized?, I had the idea of generalizing it by introducing an additional variable. I didn't manage to solve the generalized question yet, but working on it, it suddenly occurred to me a couple of days later that the additional variable provided in fact an easy answer of the initial question.