Some Polyomino Tilings of the Plane

We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the $L$ tetromino, and the $T$ tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by each of these. For the $T$ tetromino, we also derive a lower bound from the solution of the Ising model in two dimensions.