Tetromino tilings on the Tetris board*

Tetrominos, comprised of four identical squares joined together along edges, have achieved substantial popular recognition as the elemental components of the widely known game, Tetris. In this paper, we present a recursive formula aimed at exact enumeration of tetromino tilings on a rectangular board with dimensions m x n. Furthermore, we modify the tiling criterion to mirror the Tetris gameplay, resulting in what we term Tetris tiling of height n. By employing this adjusted condition, we accurately calculate the total number of Tetris tilings. Additionally, the asymptotic behavior of the growth rate associated with the tetromino tiling is discussed.