Harry's acceptance letters' count sequence

After ignoring the first letter, Harry was sent another one. Then 3, 12, 24. So the sequence would be 1, 1, 3, 12, 24, ...

Obviously, there are many sequences starting with these numbers. Is there any algorithm behind this? Since many muggles get those letters, and surely not all parents are keen on letting their children go to Hogwarts, I think we shouldn't think of this as random Harry-specific numbers. Let's get to the bottom of this!