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December 1st, 2018, 01:31 PM   #1
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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 'n-1' letters to write such that we don't write the illegal ones.


I know that means we have $a_{n-1}$ combinations after $C$.
But that is what I don't understand, what is that $a_{n-1}$, how do we know it really contains only the legal combinations?


I wold love to get some sense of this concept.


Thanks.
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December 2nd, 2018, 02:55 PM   #2
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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.
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