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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 Fibonacci-Automatic Words, III: Enumeration and Abelian Properties, Intl. J. Found. Comput. Sci. 27 (2016), 943-963.

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

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Last modified September 27 19:04 EDT 2020. Contains 337388 sequences. (Running on oeis4.)