Some new identities of generalized Fibonacci and generalized Pell numbers via a new type of numbers

TL;DR

This paper introduces a new class of generalized numbers to derive novel identities for generalized Fibonacci and Pell numbers, unifying and extending known identities involving classical sequences.

Contribution

It proposes a new type of generalized numbers and derives new identities, including special cases of existing identities, for Fibonacci, Pell, Lucas, and Pell-Lucas numbers.

Findings

New identities for generalized Fibonacci and Pell numbers

Unification of existing identities as special cases

Extension of identities involving classical sequences

Abstract

This paper is concerned with developing some new identities of generalized Fibonacci numbers and generalized Pell numbers. A new class of generalized numbers is introduced for this purpose. The two well-known identities of Sury and Marques which are recently developed are deduced as special cases. Moreover, some other interesting identities involving the celebrated Fibonacci, Lucas, Pell and Pell-Lucas numbers are also deduced