A334831 Number of binary words of length n that avoid abelian 4th powers circularly.

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

Offset: 1

Author

Jarkko Peltomäki, May 13 2020

Keywords

• nonn
• more

Comments

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.

Examples

			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.
		

Links

• Jarkko Peltomäki, Markus A. Whiteland, Avoiding abelian powers cyclically, arXiv:2006.06307 [cs.FL], 2020.

Crossrefs

Cf. A305003, A305594.