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It sounds like he's experiencing a reverse or inverted sneeze. The dog will honk, sounds like he's sucking in and trying to push something from the noses.
It's as harmless as a normal sneeze and has the same reason for being. It clears the nose of irritants.
You might want to take a look around and see if there are any irritants like carpet powder or cleaners.
Let me know if you have more questions.