It's more of a double-take on the inhale. 1) Inhale 2) Microscopic pause 3) Inhale some more 4) Exhale longer than inhaling.

From what I've noticed, more than two inhales is fine, it still works. It just shouldn't be an uncomfortable amount of air in the lungs.

I've also noticed that my dog does this when he's about to go to sleep.

yeah basically it is how you breathe after sobbing intensely.