# Properties of Periodic Fibonacci-like Sequences

## 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.

## Key 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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Source: https://tomesphere.com/paper/1701.08566