Buy him a seat. You'll be very glad to have the space. We found that the car seat made us a bit squished and got the person in front of us kicked a lot, but my son did have an easier time sleeping. It's just when he wanted to be out of the seat (which for a 3+ hour plane ride will certainly happen at some point) that things were really tight. But still better than if he were on your lap the whole time!!
If you do bring the car seat on, ask the flight attendent for a seat-belt extender. It makes getting the car seat properly buckled in much, much easier.
A clipboard with plenty of paper and crayons and stickers kept our kids entertained as toddlers, both on planes and car-trips, for a while anyway, and the clipboard gives something hard to write on but avoids the inevitable banging on the tray-table.
By the way, we found the GoGoKidz wheels that attach to the carseat to be a life-saver for traveling!