A336487 Numbers m such that the Fibonacci word (A003849) has an abelian cube of order m.

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

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: A084116 A137620 A368999 * A028765 A181807 A059870

Adjacent sequences: A336484 A336485 A336486 * A336488 A336489 A336490

Keyword

nonn

Author

Jeffrey Shallit, Jul 23 2020

Status

approved