Properties of Periodic Fibonacci-like Sequences
Alexander V. Evako
TL;DR
This paper investigates the properties of generalized Fibonacci-like sequences, demonstrating that they are periodic under specific conditions related to their parameters, which has implications for finite difference methods in PDEs.
Contribution
It provides a theoretical analysis showing the conditions under which generalized Fibonacci-like sequences are periodic, expanding understanding of their behavior in numerical methods.
Findings
Sequences are periodic when C=-1 and |B|<2.
Period T is greater than 2.
Sequence properties depend on parameters A, B, C.
Abstract
Generalized Fibonacci-like sequences appear in finite difference approximations of the Partial Differential Equations based upon replacing partial differential equations by finite difference equations. This paper studies properties of the generalized Fibonacci-like sequence F_(n+2)=A+BF_(n+1)+CF_n. It is shown that this sequence is periodic with the period T>2 if C=-1,|B|<2.
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