2022/03/17 by Nathan A. Fox, Fox, Nathan · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #05C05 #11B37 (Primary) #11B39 #11Y16 (Secondary) #Advanced Mathematical Theories and Applications #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2203.09340
openalex publication_date 2022/03/17 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward descriptions in terms of how often each value in the sequence occurs. In this paper, we generalize the most classical examples to a larger family of sequences parametrized by linear recurrence relations. Each of our sequences can be constructed in three different ways: via a nested recurrence relation, from labeled infinite trees, or by using Zeckendorf-like strings of digits to describe its frequency sequence. We conclude the paper by discussing the asymptotic behaviors of our sequences.