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sheep

In sheep talk the only letters used are B and A. Sequences of words are formed as follows:

The first word only contains the single letter A.

To get the next word in the sequence change each A in the previous word into B and each B in the previous word into AB.

Write down the first ten words in this sequence.

Count the number of A's in each word in the sequence. Then count the number of B's in each word in the sequence. Finally count the number of letters in each word in the sequence. You now have three sequences of numbers. What do you notice? Will the same patterns continue if you generate longer sequences of words?