I would like to find an equation in which, given a number n, you can find the amount of ways to add 1, 2, and 3 to create the number. The commutative rule doesn’t apply; for example, 1 + 1 + 3 is a different arrangement than 1 + 3 + 1.

Let’s take the number 4 for an example. There are 7 ways to combine the numbers 1, 2, and 3 to create 4:

1 1 1 1

1 1 2

1 2 1

2 1 1

1 3

3 1

2 2

Any ideas?