Emilia

import Data.Sequence as Q
main = interact $ unlines . map show . solve . flip Q.replicate 'A' . read
solve q = Q.length q : go q where
  go q | Q.length q < 2 = []
       | ('A',q') <- nom q = go (q' <> Q.fromList "BC")
       | otherwise = go' q
  go' q | (c,q') <- nom q = case c of 'B' -> go' (q' |> 'A')
                                      'C' -> go' (q' >< Q.fromList "AAA")
                                      _ -> solve q
  nom q = (c,q'') where (c :< q') = Q.viewl q
                        q'' = Q.drop 1 q'