OFFSET
0
COMMENTS
This is an aperiodic sequence that avoids the pattern x x x^R, where x is a nonempty block and x^R denotes the reversal of x.
It can be generated as the limit of the words R(i), where R(0) = 0, R(1) = 00, and R(n) = R(n-1)R(n-2) if n == 0 (mod 3), and R(n) = R(n-1) c(R(n-2)) if n == 1, 2 (mod 3), where c flips 0 to 1 and vic-versa.
It can also be generated as the image, under the coding that maps a, b -> 0 and c, d -> 1, of the fixed point (see A316340), starting with a, of the morphism a -> abcab, b -> cda, c -> cdacd, d -> abc.
LINKS
Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, A Taxonomy of Morphic Sequences, arXiv preprint arXiv:1711.10807, Nov 29 2017
C. F. Du, H. Mousavi, E. Rowland, L. Schaeffer, J. Shallit, Decision algorithms for Fibonacci-automatic words, II: related sequences and avoidability, preprint, February 10 2016.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, May 16 2016
STATUS
approved