Number Factors

Statement

Given a fixed list of numbers, $[1, 3, 4]$, and a target number, $n$, count all the possible ways in which $n$ can be expressed as the sum of the given numbers. If there is no possible way to represent $n$ using the provided numbers, return $0$.

Note: You may assume that you can use a specific number as many times as you want. Additionally, the order in which we select numbers from the list is significant.

Let's say $n$ is 4, then using the given numbers, $1$, $3$, and $4$, the target number $n$ can be expressed in the following four ways:

• Using $1$ four times: $1+1+1+1 = 4$.

• Using a $1$ and then a $3$: $1 + 3 = 4$.

• Using a $3$ and then a $1$: ...