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Good Word Sequence Letters Count

2050SpecialistCombinatoricsAlgebraCounting Principles

AIME II · 2003 · Problem 3

Define a $\text{good word}$ as a sequence of letters that consists only of the letters $A$, $B$, and $C$ - some of these letters may not appear in the sequence - and in which $A$ is never immediately followed by $B$, $B$ is never immediately followed by $C$, and $C$ is never immediately followed by $A$. How many seven-letter good words are there?
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