My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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.
wilhelm is offline  
 
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).
Hoempa is offline  
Reply

  My Math Forum > College Math Forum > Applied Math

Tags
conditions, consisting, number, satisfying, words



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find x values satisfying the condition Drake Algebra 6 April 11th, 2013 10:30 AM
Find all functions satisfying the equation PaulinaAnna Algebra 16 December 16th, 2010 04:38 PM
An engineering system consisting of n components varunnayudu Advanced Statistics 3 December 6th, 2010 01:17 PM
Number of conditions when 12 variables available DonnaS Calculus 2 November 1st, 2009 04:08 PM
QUESTION on a reduced residue system consisting of squares. shangwen_ren Number Theory 1 September 28th, 2009 10:59 AM





Copyright © 2019 My Math Forum. All rights reserved.