Tromino tilings of domino-deficient rectangles

We consider tromino tilings of m×n domino-deficient rectangles, where 3|(mn−2) and m,n≥0, and characterize all cases of domino removal that admit such tilings, thereby settling the open problem posed by Ash and Golomb in J. Marshall Ash, S. Golomb, Tiling Deficient Rectangles with Trominoes, Integre Technical Publishing Co., Mathematics Magazine (2003), 46-55]. We suggest a procedure for tiling domino-deficient rectangles based on this characterization. We also consider general 2-deficiency in n×4 rectangles, where n≥8, and characterize all pairs of missing squares which do not permit a tromino tiling.