A 2 x n checkerboard is to be tiled using two types of tiles. The first...

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A 2 x n checkerboard is to be tiled using two types of tiles. The first tile is a 1 x 1 square tile. The second tile is called an L-tile and is formed by removing the upper-right 1 x 1 square from a 2 x 2 tile. The L-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) denote the number of tilings of the 2 x n checkerboard using 1 x 1 tiles and L-tiles. Find a recursive formula for t(n) and use it to determine t(7). A 2 x n checkerboard is to be tiled using two types of tiles. The first tile is a 1 x 1 square tile. The second tile is called an L-tile and is formed by removing the upper-right 1 x 1 square from a 2 x 2 tile. The L-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) denote the number of tilings of the 2 x n checkerboard using 1 x 1 tiles and L-tiles. Find a recursive formula for t(n) and use it to determine t(7).