# A note on Modified Third-order Jacobsthal numbers

## TL;DR

This paper introduces the modified third-order Jacobsthal sequence, explores its properties including a Binet-style formula and generating function, contributing to the mathematical understanding of this sequence.

## Contribution

It defines a new variant of the third-order Jacobsthal sequence and derives its fundamental properties, such as formulas and generating functions.

## Key findings

- Derived the Binet-style formula for the sequence
- Established the generating function for the sequence
- Provided properties and relations involving the sequence

## Abstract

Modified third-order Jacobsthal sequence is defined in this study. Some properties involving this sequence, including the Binet-style formula and the generating function are also presented.