Suppose you have 5 kinds of wooden blocks: red blocks which are 2 inches high, b

Question

Suppose you have 5 kinds of wooden blocks: red blocks which are 2 inches high, blue blocks which are 2 inches high, green blocks which are 2 inches high, yellow blocks which are 3 inches high, and violet blocks which are 3 inches high. Let tn be the number of ways to build a tower of blocks n inches high by placing blocks one on top of another. Assume you have an unlimited number of each kind of block. Find a recurrence relation and initial conditions for tn Use this recurrence relation to compute the number of ways to build a tower 6 inches high. Find an explicit formula for tn. Use your formula to compute the number of ways to build a tower 21 inches high and simplify your answer to a single number. Your formula should be in terms of fractions, not decimals. Find a closed form for the generating function T(x) = (Recommendation: expand your series and make sure that it agrees with the specific value you got in part b.)

Explanation / Answer

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