

A336487


Numbers m such that the Fibonacci word (A003849) has an abelian cube of order m.


0



0, 2, 3, 5, 6, 7, 8, 10, 11, 13, 15, 16, 18, 19, 21, 23, 24, 26, 27, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 44, 45, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 62, 63, 65, 66, 68, 70, 71, 73, 74, 76, 78, 79, 81, 82, 83, 84, 86, 87, 89, 91, 92, 94, 95, 96, 97, 99
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

An abelian cube is three consecutive blocks x x' x'' of the same length and having the same number of occurrences of each letter. For example, "deeded" is an abelian cube. The order of an abelian cube x x' x'' is the length of x.


LINKS

Table of n, a(n) for n=1..67.
C. F. Du, H. Mousavi, L. Schaeffer, and J. Shallit, Decision Algorithms for FibonacciAutomatic Words, III: Enumeration and Abelian Properties, Intl. J. Found. Comput. Sci. 27 (2016), 943963.


EXAMPLE

For m = 1 neither 000 nor 111 appears in the Fibonacci word, so 1 is not a term.
But for m = 2 the word 101001 appears, so 2 is a term.


CROSSREFS

Sequence in context: A072510 A084116 A137620 * A028765 A181807 A059870
Adjacent sequences: A336484 A336485 A336486 * A336488 A336489 A336490


KEYWORD

nonn


AUTHOR

Jeffrey Shallit, Jul 23 2020


STATUS

approved



