Mock AIME 3 Pre 2005 Problems/Problem 5
In Zuminglish, all words consist only of the letters 
and 
. As in English, 
is said to be a vowel and 
and are consonants. A string of 
and 
is a word in Zuminglish if and only if between any two 
there appear at least two consonants. Let 
denote the number of 
-letter Zuminglish words. Determine the remainder obtained when is divided by 
.
