排列組合，定義“好字”為由三個字母A、B、C所組成的序列

定義一個“好字”為由三個字母A、B、C所組成的序列（A、B、C不必全部出現在序列中），其中A不能緊接在B之後，B不能緊接在C之後且C不能緊接在A之後。求六個字母的“好字”共有____個。

第一字方法 為 3
第二字方法 為 2
...
第六字方法 為 2

\( 3 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2  =96 \)

幫忙補上出處
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)
這裡可以下載2003AIME中文版題目
http://forum.nta.org.tw/examservice/showthread.php?t=52834
http://forum.nta.org.tw/examserv ... =229485&postcount=5