Domino and Tromino - Profile States

For $2$ rows, the profile between columns can be: $00$ (both rows end at the same column), $01$ (row $0$ ends earlier, row $1$ sticks out), or $10$ (row $1$ ends earlier, row $0$ sticks out).

That's $3$ states per column. State $00$ means both rows are flush. From here, you can place a vertical domino, two horizontal dominoes, or a tromino (which creates an uneven profile). State $01$ means row $1$ has a protruding cell you must cover. You can place a tromino to fill it and make the profile $10$, or place a horizontal domino in row $1$ to bring it flush to $00$.