Linear Recurrent Subsequences of Meta-Fibonacci Sequences
Nathan Fox

TL;DR
This paper proves that all linear recurrent sequences with positive coefficients can be embedded within solutions of meta-Fibonacci sequences, answering a previously open question.
Contribution
It establishes that every linear recurrent sequence with positive coefficients can occur as a solution of a meta-Fibonacci sequence, expanding understanding of their relationship.
Findings
Confirmed the existence of meta-Fibonacci solutions for all positive-coefficient linear recurrences.
Extended the theoretical framework connecting linear recurrences and meta-Fibonacci sequences.
Provided a constructive proof for the embedding of linear recurrences in meta-Fibonacci sequences.
Abstract
In a recent paper, Frank Ruskey asked whether every linear recurrent sequence can occur in some solution of a meta-Fibonacci sequence. In this paper, we answer his question in the affirmative for recurrences with positive coefficients.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Theories and Applications · semigroups and automata theory · Mathematics and Applications
