...

$$3 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 =96$$

Define a 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?
(2003AIME，http://www.artofproblemsolving.c ... 82&cid=45&year=2003)