# On a four-parameters generalization of some special sequences

## TL;DR

This paper introduces a new four-parameter sequence that generalizes several classical integer sequences, providing combinatorial interpretations, identities, and a Cassini formula, enriching the understanding of these sequences.

## Contribution

It presents a novel four-parameter sequence unifying multiple well-known sequences, along with derived identities and combinatorial interpretations.

## Key findings

- Derived identities for classical sequences from the new sequence
- Provided combinatorial interpretations of the new sequence
- Established a Cassini formula for the new sequence

## Abstract

We introduce a new four-parameters sequence that simultaneously generalizes some well-known integer sequences, including Fibonacci, Padovan, Jacobsthatl, Pell, and Lucas numbers. Combinatorial interpretations are discussed and many identities for this general sequence are derived. As a consequence, a number of identities for Fibonacci, Lucas, Pell, Jacobsthal, Padovan, and Narayana numbers as well as some of their generalizations are obtained. We also present the Cassini formula for the new sequence.