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, 38080, 7272, 51504, 54910, 79092, 51360, 200572, 70854, 260408, 147224, 541080, 301300, 472068, 385920

Offset

1,1

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.

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..70

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

Example

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.

Crossrefs

Cf. A305003, A305594.

Sequence in context: A033748 A033736 A033760 * A320231 A320232 A320233

Adjacent sequences: A334828 A334829 A334830 * A334832 A334833 A334834

Keyword

nonn

Author

Jarkko Peltomäki, May 13 2020

Extensions

More terms from Bert Dobbelaere, Nov 17 2025

Status

approved