
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
December 1st, 2018, 12:31 PM  #1 
Newbie Joined: Nov 2018 From: France Posts: 8 Thanks: 0  Find a recursive formula for the number of combinations
I have some question integrating between combinatorics and recursive formulas. Generally, I have some difficulty with the concept of recursion, as well as with the recursion in programming unfortunately. I have some question to solve, and maybe you can guide me: Find a recursive formula and a terminal condition for the number of words with the length 'n' that can be written by $A, B, C$, such that these combinations won't be shown: $AB, AC, BA, BC$. Now, I know that if we start from $A$ or $B$ we of course have one option, 'n' $A's$, 'n' $B's$  which are two combinations. Now, if we start from $C$, I understand we have more 'n1' letters to write such that we don't write the illegal ones. I know that means we have $a_{n1}$ combinations after $C$. But that is what I don't understand, what is that $a_{n1}$, how do we know it really contains only the legal combinations? I wold love to get some sense of this concept. Thanks. 
December 2nd, 2018, 01:55 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 
I am not sure I grasp the problem. Is CA allowed or not? If not why not? How about ZAC? You seem to be thinking along the lines that the string must proceed in alphabetical order. 

Tags 
combinations, find, formula, number, recursive 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Find number of elements combinations covered by a given set  grigor  Applied Math  0  March 25th, 2014 11:25 PM 
recursive formula  bongantedd  Algebra  7  September 21st, 2013 11:43 PM 
Find number of combinations2  Girish.Talele  Algebra  5  January 2nd, 2013 09:12 PM 
Find number of combinations  Girish.Talele  Algebra  2  January 1st, 2013 10:52 PM 
Find non recursive formula for the fibonacci sequence  Airmax  Number Theory  5  May 29th, 2009 08:58 PM 