Question: Let (a_n) be the sequence defined by a_0 = 0, a_1 = 12, and for n 2, a_{n+1} = 4a_n +5a_{n1}. Find a closed formula

Let (a_n) be the sequence defined by a_0 = 0, a_1 = 12, and for n 2, a_{n+1} = 4a_n +5a_{n1}. Find a closed formula for a_n.Suppose we want to tile a 1n board of squares using either square 11 tiles and/or 12 domino tiles. However, suppose also that our square tiles can be either red, green, or blue, and our domino tiles can be either orange or purple. Different colors count as different tilings. Let Tn be the number of tilings of this board. (a) (4 points) Determine the number of possible tilings for n = 1, 2, 3, 4. (b) (8 points) Find a recurrence relation for Tn and prove this recurrence relation holds

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