Can a paradiddaloid have a single tap as one of its patterns?

Absolutely! A single tap epitomizes the goal of rapid back-and-forth movement between patterns. Notable examples include Paradiddaloid 2 and Paradiddaloid 3.

When we use a single-tap pattern, it is imperative that we specify the note value of the tap, as changing the note value will change the paradiddaloid as a whole.

To illustrate this point, let's tinker with Paradiddaloid 3 and see what happens. Here's the notation for Paradiddaloid 3 – the single tap corresponds to Pattern A, which in turn corresponds to the first, fifth, sixth, and tenth notes:

Now, suppose we change the single tap from an eighth note to a sixteenth note.

Alternatively, what if we change the single tap from an eighth note to a quarter note?

So, we can see that the note value of a single-tap pattern used in the construction of a paradiddaloid can have a dramatic impact on the final product.