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%I #15 Sep 04 2020 21:25:23
%S 2,2,6,8,10,6,28,0,36,120,132,168,364,112,390,32,374,396,114,280,756,
%T 462,92,1584,1100,910,2484,2352,3016,3270,10292,5824,12804,12240
%N Number of binary words of length n that avoid abelian 4th powers circularly.
%C 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.
%H Jarkko Peltomäki, Markus A. Whiteland, <a href="https://arxiv.org/abs/2006.06307">Avoiding abelian powers cyclically</a>, arXiv:2006.06307 [cs.FL], 2020.
%e 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.
%Y Cf. A305003, A305594.
%K nonn,more
%O 1,1
%A _Jarkko Peltomäki_, May 13 2020