A "square" word consists of two identical adjacent subwords (for example, acbacb). A squarefree word contains no square words as subwords (for example, abcacbabcb). The only squarefree binary words are a, b, ab, ba, aba, and bab (since aa, bb, aaa, aab, abb, baa, bba, and bbb contain square identical adjacent subwords a, b, a, a, b, a, b, and b, respectively). However, there are arbitrarily long ternary squarefree words. The number s(n) of ternary squarefree words of length n = 1, 2, ... are 1, 3, 6, 12, 18, 30, 42, 60, ... (OEIS A006156), and s(n) is bounded by 6·1.032^n<=s(n)<=6·1.379^n (Brandenburg 1983).

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