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A334831
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Number of binary words of length n that avoid abelian 4th powers circularly.
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0
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2, 2, 6, 8, 10, 6, 28, 0, 36, 120, 132, 168, 364, 112, 390, 32, 374, 396, 114, 280, 756, 462, 92, 1584, 1100, 910, 2484, 2352, 3016, 3270, 10292, 5824, 12804, 12240
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OFFSET
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1,1
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COMMENTS
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A word w of length n avoids abelian K-th powers circularly if every abelian K-th power in w^{K+1} has a block length of at least n. An abelian 4th power means a concatenation of four blocks that are permutations of each other, e.g., (011)(101)(110)(101) is an abelian 4th power of block length 3.
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LINKS
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EXAMPLE
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a(6) = 6, and the words are 000111, 001110, 011100 and their complements. The word w = 010011 does not avoid abelian 4th powers circularly because w^3 has abelian 4th power of period 2 starting at position 6.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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