winning configurations Part II --more complex polyominos -- tetris pieces

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How many ways can the 2x2n (tube) board be tiled or filled with Tetris Pieces ? This is similar to other tilings except the Tetris pieces have 4 squares and have more complex configurations. The proof is a similar use of Recurrence equations then more simpler Polyominos. It has not been added to this math problem data base so thought we should add it. The reccurance is Fn^2