2019/10/17 by Kevin G. Hare, Hare, Kevin, JOHN C. SAUNDERS +1
Computer Science · #Algorithms and Data Compression #Cellular Automata and Applications #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1910.07824
openalex publication_date 2019/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference of the two preceding terms where the pluses and minuses follow a certain pattern. In 2012, McLellan proved that if the pluses and minuses follow a periodic pattern and Gn is the nth term of the resulting generalised Fibonacci sequence, then limn→∞|Gn|1/n exists. We extend her results to recurrences of the form Gm+2 = αm Gm+1 ± Gm if the choices of pluses and minuses, and of the αm follow a balancing word type pattern.