14 yr old son was in state custody for <6 mo. due to his criminal activity. We paid child support during this time. Am I able to say he lived with us for the whole year?

My 14 year old son was in states custody for just under 6 months out of the year due to his criminal activity.  Part of the time he was in a detention program and the rest was in a group home.  My husband and I were required to pay child support during this time.  Am I still able to indicate that he lived with us for the whole year since we paid the child support?