Some Fibonacci-Related Sequences
Combinatorics
2024-01-03 v3 Discrete Mathematics
Formal Languages and Automata Theory
Abstract
We discuss an interesting sequence defined recursively; namely, sequence A105774 from the On-Line Encyclopedia of Integer Sequences, and study some of its properties. Our main tools are Fibonacci representation, finite automata, and the Walnut theorem-prover. We also prove two new results about synchronized sequences.
Cite
@article{arxiv.2312.11706,
title = {Some Fibonacci-Related Sequences},
author = {Benoit Cloitre and Jeffrey Shallit},
journal= {arXiv preprint arXiv:2312.11706},
year = {2024}
}