***** NOT A TEACHER *****
Hello, D.C. Foster:
One expert has a very simple "rule": no + noun. In other words, never use an article between "no" and its noun:
"There is no sofa in the living room."
That expert reminds us that verb + not CAN use an article:
"There is not a sofa in the living room."
That expert tells us that the no + noun construction (kind of sentence) is more EMPHATIC:
James: May I borrow your car for the weekend?
Mona: I am sorry, but I do not have a car.
James: I do not believe you. I saw you driving a Honda yesterday.
Mona: That was not my car.
James: Are you sure?
Mona: Listen, James. I have no car!
That expert is Michael Swan in his Practical English Usage.
P.S. If you are looking for a more in-depth answer, you should remember that "not" is an adverb and that "no" is an adjective (in traditional grammar terms).