Counting dimer tilings

A dimer is a 2×1 domino-shaped rectangle. How many ways are there to arrange four non-overlapping dimers on a 3×3 grid, leaving one of the 9 spaces empty? The three essentially different ways to do this are shown in the picture above. If the centre square is left blank, then the four dimers must be arranged as in the picture on the left, or its mirror i…