# On a new formula for the number of unrestricted partitions

## TL;DR

This paper introduces a novel formula for calculating the number of unrestricted partitions of an integer n, linking it to solutions of specific systems of equations involving natural numbers.

## Contribution

It presents a new mathematical formula connecting unrestricted partitions to solutions of systems of equations, offering a fresh approach to partition enumeration.

## Key findings

- Derived a new formula for unrestricted partitions
- Established a correspondence with solutions of systems of equations
- Provides a potential new method for partition counting

## Abstract

In this paper we present a new formula for the number of unrestricted partitions of $n$. We do this by introducing a correspondence between the number of unrestrited partitions of $n$ and the number of non-negative solutions of systems of two equations, involving natural numbers in the interval (1 $,n^{2}$).