'A(n)': ellipsis of the indefinite article repeated in different forms

This is a matter of style. Here’s one (emphasis added):

5.79: Articles with coordinate nouns

In a series of coordinate nouns, an article may appear before each noun, but it is not necessary when the same type of article (definite or indefinite) applies to each noun {the rosebush and hedge need trimming}. If the things named make up a single idea, it’s especially unnecessary to repeat the article {in the highest degree of dressage, the horse and rider appear to be one entity}. And if the named things are covered by one plural noun, the definite article should not be repeated {in the first and second years of college}. But if you want to distinguish concepts or add emphasis, then do repeat the article {the time, the money, and the effort were all wasted}. For indefinite articles, you may use or omit the article before each subsequent noun {fruit salad needs an orange, a mango, and a banana} {bring a raincoat, hat, and umbrella}. In the last example, the first two items would take a while the last would take an, but only the first item need be matched with a or an {bring an umbrella, raincoat, and hat}.

_{Source: The Chicago Manual of Style (login required)}