I prefer your very complete answer to my very simple one !!Hi EnglishBug,
To expand on Spira's answer, which I agree with:
It is mandatory to leave out the second article when the two objects listed are part of an indivisible whole or set: I'd like a gin and tonic. Do you have a mortar and pestle, and so on. It is mandatory to include the article when the objects are thought of as different categories: I'd like a beer and a hamburger. I went to the store and I bought a watermelon and a roll of toilet paper...
"A pencil and pad" could logically go together as a set, but could also be thought of as separate objects, so the repeated article is optional here.