Using the indefinite article after no and not

Question

I was wondering if someone could help explain why we don't use the indefinite article in this sentence

There is no couch in the living room

but we do use it in this sentence

There isn't a couch in the living room?

Now I know it has something to do with no vs. not but I can't figure out how to explain to people why there is a difference.

Also, when I think about it, it seems like we almost never use 'a' after no but we do after not... but again, I just came seem to come up with a rule to explain it?

Thanks kindly....

Answer 1

'No' as a determiner means 'not a/not one/not any'. If we said 'no a couch', we would effectively be saying 'not a a couch'.

More formally, 'no' and 'a' are central determiners, and central determiners are mutually exclusive - they cannot co-occur, as Sylvia Chalker notes in The Oxford Companion to the English Language (1992).