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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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