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Cubefree Word

A cubefree word contains no cubed words as subwords. The number of binary cubefree words of length n=1, 2, ... are 2, 4, 6, 10, 16, 24, 36, 56, 80, 118, ... (OEIS A028445). Binary cubefree words satisfy

2·1.080^n<=c(n)<=2·1.522^n.

The number of ternary cubefree words of length n=1, 2, ... are 3, 9, 24, 66, 180, 486, 1314, ... (OEIS A051042). The number of quaternary cubefree words of length n=1, 2, ... are 4, 16, 60, 228, 864, 3264, 12336, ... (OEIS A051043).

See also

Overlapfree Word, Reverend Back's Abbey Floor, Squarefree Word, Word

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References

Allouche, J.-P. and Shallit, J. "Repetition in Words." §1.6 in Automatic Sequences: Theory, Applications, Generalizations. Cambridge, England: Cambridge University Press, pp. 14-16, 2003.Finch, S. R. "Pattern-Free Word Constants." §5.17 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 367-371, 2003.Sloane, N. J. A. Sequences A028445, A051042, and A051043 in "The On-Line Encyclopedia of Integer Sequences."

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Cubefree Word

Cite this as:

Weisstein, Eric W. "Cubefree Word." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CubefreeWord.html

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