Finding Total Number of Electron States with n=3

[roeb]

Homework Statement

n = 3
Using the fact that there are two quantum states for each value of l and m because of electron spin. Find the total number of electron states with n = 3.

Homework Equations

The Attempt at a Solution

I've already determined that l = 0, 1, 2
and m = -2, -1, 0, 1, 2

So, given the information I figured it would be 8 * 2 = 16 quantum states.
Unfortunately, it's supposed to be 18 quantum states and I fail to see where they pick up 2 extra ones. Does anyone know what I am doing incorrectly?

 

[loonychune]

Well for n = 3...

Set l = 2:
then m can take on the range of: -2,-1,0,1,2

Set l = 1:
m = {-1,0,1}

l = 0:
m = 0

There's 9 states.

EDIT: Think of, for n = 3, every independent quantum state by labelling your state:

$$\psi_{n,l,m}: \psi_{3,0,0} \neq \psi_{3,1,-1} \neq \psi_{3,1,0}$$

and so on..