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).
