Guten Tag PaulS108,
Thank you for your question!
You will sometimes find that when having a long list of nouns (2 or more) related to the same context and connected with und, Germans omit some or all articles. This is sometimes but not always possible as it can change the way you sound as well as the entire meaning of the sentence.
So for example, “Das Haus hat Doppelzimmer, Einzelzimmer, Wohnzimmer und Terrasse.” - “The house has (a) double room, (a) single room, (a) living room and (a) patio.” would be perfectly fine to say.
But watch out for sentences like “Er hat mit dem Architekten und Bauleiter gesprochen.” - “He talked to the architect and the project manager.” This could lead to misunderstandings because the sentence has two possible meanings: He talked to both the architect and the project manager (two different people) or he talked to the architect who is also the project manager.
In the sentence above it doesn't really change the meaning, it just makes it a bit smother to read as you don't stumble over all the articles.
When a noun is defined more closely with an adjective however, it needs an article ("…und eine wunderschöne Terrasse").
In cases where there is a strong connection between two nouns joint together with a preposition, an article is often not needed/optional ("Wohnzimmer mit Kochnische"). You can see the second noun as a description of the first one. A few other examples would be:
“Ich hätte gerne ein Zimmer mit/ohne Balkon.” - “I would like a room with/without a balcony.”
“Ein Zimmer mit Meeresblick wäre schön.” - “A room with an ocean view would be nice.”
In saying all that, it would also be perfectly fine to make use of all the articles in your sentence:
“Das Haus hat ein Doppelzimmer und zwei Einzelzimmer, ein Wohnzimmer mit einer Kochnische und eine wunderschöne Terrasse.”
I hope this helps.