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hw1 - (a Find a recurrence relation for the sequence A n(b...

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Math 146: Algebraic Combinatorics Homework 1 This problem set is due Friday, April 2. Do problems 1.1(c,d,g) and 1.3(a,c,g,k), in addition to the following: GK1.1. Let A n be the number of sequences of letters (or “words”, although they don’t have to be in the dictionary) of width n in the letters A, W, and M, where A has width 1 while M and W have width 2. For example, MAW has width 5.
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Unformatted text preview: (a) Find a recurrence relation for the sequence ( A n ) . (b) Guess a formula for A n . (Hint: Multiply by 3 first.) (c) Prove it directly. (d) Find the ordinary generating function for this sequence. (e) Express the ordinary generating function using partial fractions. (f) Use the partial fraction expression to give another proof of the formula. 1...
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