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November, 2013

9 November
Posted in Article, Math Problems

Counting Words

Suppose that we are given the alphabet \Sigma = \Rec{0,1,2}; a word of length n: x_n \in \Sigma^5, is an ordered n-tuple whose elements all came from \Sigma. For example, a word of length 5 in \Sigma might be the tuple (0,0,2,1,0), which we will hereon denote as 00210. For some natural number k \le n, how many words of length n are there that contains exactly k zeros?

6 November

Annoying Mclaurin Series

Suppose that we’re given the function B(z) = \frac{1 + z}{1 - z - z^2}, find the ordinary generating function associated with it in the form of B(z) = \sum_{k=0}^\infty b_k k^z. Furthermore, find/compute \sigma_n = \sum_{k=0}^n b_k.