A338298 First difference of the subword complexity function of the Fibonacci-Thue-Morse sequence (A095076).

1, 2, 4, 6, 10, 6, 6, 8, 6, 8, 8, 6, 6, 6, 6, 8, 8, 8, 6, 6, 6, 6, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset

0,2

Comments

The subword complexity function of a sequence is the number of distinct blocks of length n occurring in the sequence.

Links

Table of n, a(n) for n=0..85.

Michel Dekking, The structure of Zeckendorf representations and base phi expansions, talk for the One World Seminar on Combinatorics on Words, October 19 2020.

Jeffrey Shallit, Subword complexity of the Fibonacci-Thue-Morse sequence: the proof of Dekking’s conjecture, arXiv:2010.10956 [cs.DM], 2020.

Formula

For all n >= 7, the sequence takes only the values 6 and 8, in longer and longer intervals that are of length a Fibonacci number, or a Fibonacci number +- 1. For the exact statement, see the paper of Shallit.

Crossrefs

Cf. A095076.

Sequence in context: A227526 A093081 A242521 * A366581 A073659 A073661

Adjacent sequences: A338295 A338296 A338297 * A338299 A338300 A338301

Keyword

nonn

Author

Jeffrey Shallit, Oct 21 2020

Status

approved