Secondary Air Injection. Read up on it. It's normal.
Having an issues with a 06 A3 3.2. Car has 96K miles on it. On cold starts the car will run rough for around 30 seconds then it will smooth out. If the car sits for a period of more than few days, it will also induce a rough cold start. No DTCs stored or Cam timing issues. Car will idle normal if driven regularly.
Faulty injectors maybe?