# On the properties of new families of generalized Fibonacci numbers

## TL;DR

This paper introduces new families of generalized Fibonacci and Lucas numbers, providing their recurrence relations and generating functions specifically for the case when k=2, expanding the mathematical understanding of these sequences.

## Contribution

The paper presents novel families of generalized Fibonacci and Lucas numbers along with their recurrence relations and generating functions for k=2, which were not previously documented.

## Key findings

- New families of generalized Fibonacci and Lucas numbers introduced.
- Recurrence relations for these new families derived.
- Generating functions for the case k=2 provided.

## Abstract

In this paper, new families of generalized Fibonacci and Lucas numbers are introduced. In addition, we present the recurrence relations and the generating functions of the new families for $k=2$.