That's excessive (old protocol). I would make the 16 wk shot the last one, then do rabies at 18 wks (or when your state law mandates but not at the same time as the puppy shot).
Because puppy is still protected by mother... She wouldn't have done early ones... Said that I should have done at 12, 16 weeks and 20 weeks. But because I got him at a rescue he already had the first two.
State mandates Rabies at 16 weeks.