Identities for second order recurrence sequences

TL;DR

This paper derives identities for second order recurrence sequences and applies them to analyze six well-known integer sequences, providing a unified framework for their study.

Contribution

It introduces new identities for second order recurrence sequences and unifies the analysis of six classical integer sequences using these identities.

Findings

Derived identities for second order recurrence sequences

Unified analysis of Fibonacci, Lucas, Jacobsthal, Pell, and related sequences

Enhanced understanding of relationships among these sequences

Abstract

We derive several identities for arbitrary homogeneous second order recurrence sequences with constant coefficients. The results are then applied to present a unified study of six well known integer sequences, namely the Fibonacci sequence, the sequence of Lucas numbers, the Jacobsthal sequence, the Jacobsthal-Lucas sequence, the Pell sequence and the Pell-Lucas sequence.