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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). Tags conditions, consisting, number, satisfying, words Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Drake Algebra 6 April 11th, 2013 10:30 AM PaulinaAnna Algebra 16 December 16th, 2010 04:38 PM varunnayudu Advanced Statistics 3 December 6th, 2010 01:17 PM DonnaS Calculus 2 November 1st, 2009 04:08 PM shangwen_ren Number Theory 1 September 28th, 2009 10:59 AM

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