Removing attic house fan and adding subfloor
It would be very useful if you could post a picture of what the existing framing looks like around the fan opening. 

Since it is unlikely that the joists are three feet apart there is a good chance that there are already framing headers across between two existing joists that take care of supporting the stub joist that was cut off across the fan opening. If this is the case then just one piece of 2x6 and a pair of joist hangers would be the simplest thing to add needed ceiling support back across the fan opening. 

On the other hand if the opening is different then this is where a picture comes in valuable as to offering you the best advice.