Abstract

Some Identities Involving the Generalized Lucas Numbers

Highlights

  • In the theory of numbers, the Fibonacci sequence has been always fertile ground for the mathematicians

  • There are several ways in which it has been generalized. One of these ways is by preserving the initial conditions and changing the recurrence relation

  • { } generalizations of the Lucas sequence is the class of sequences

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Summary

Introduction

In the theory of numbers, the Fibonacci sequence has been always fertile ground for the mathematicians. The terms of the sequence of Lucas numbers {Ln } can be obtained by L0 = 2, L1 =1 and the recurrence relation Ln = Ln−1 + Ln−2 ; for n ≥ 2 . One of these ways is by preserving the initial conditions and changing the recurrence relation. Whereas one more way is to preserve the recurrence relation and alternate the initial conditions.

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