A 2*n2*n checkerboard is to be tiled using two types of tiles. the first tile is a 1*11*1 square tile. the second tile is called an ll-tile and is formed by removing the upper-right 1*11*1 square from a 2*22*2 tile. the ll-tiles can be used in any of the four ways they can be rotated. (that is, the ''missing square'' can be in any of four positions.) let t (n) t (n) denote the number of tilings of the 2*n2*n checkerboard using 1*11*1 tiles and ll-tiles. find a recursive formula for t (n) t (n) and use it to determine t (7) t (7).
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