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 November 19th, 2012, 08:58 AM #1 Newbie   Joined: Nov 2012 Posts: 25 Thanks: 0 Number of words consisting of 0,1,2,3 satisfying conditions Hey. Could you help me solve the following: Find the formula (preferably a recurrence relation) for the number of words length n 1)consisting of 0,1,2 where subsequent terms (0,1,2) differ by at most 1. 2) consisting of 0,1,2,3, where 0 and 1 are not next to each other. Wilhelm.
 November 27th, 2012, 03:27 AM #2 Math Team   Joined: Apr 2010 Posts: 2,780 Thanks: 361 Re: Number of words consisting of 0,1,2,3 satisfying conditi 1) let w(n) be the amount of words with length n. Then w(0) = 1, w(1) = 3, n >= 0 gives w(n + 2) = 2 * w(n + 1) + w(n). 2) let w(n) be the amount of words with length n. Then w(1) = 4, n >= 1 gives w(n + 1) = 3 * w(n) + (4^n)/8 = 4 * w(n) - 2 * 3^(n - 1).

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