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no of words with 12 letters constructed by 2 symbols

Source: 1980 Swedish Mathematical Competition p5

March 28, 2021
combinatoricsWords

Problem Statement

A word is a string of the symbols a,ba, b which can be formed by repeated application of the following: (1) abab is a word; (2) if XX and YY are words, then so is XYXY; (3) if XX is a word, then so is aXbaXb. How many words have 1212 letters?
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