Average hitpoints on level up

I want to play the game on the core rules, but with forced average hit point rolls on level up. For mages 1d4 they'd get 2.5 hit points per level. Since the game doesn't handle fractions well, I thought I'd make it so mage gets 2 on odd levels and 3 on even levels. However, this doesn't exactly solve the problem with multiclasses, because the hitpoints are divided by 2 or 3 which messes up the average.

So my question is, what is the exact formula of hit points per level up on multiclass characters? Including rounding errors, con bonuses etc., so I could come up with good way to get average hitpoints on level up for all classes. Is it just on each level up hitdice/3 rounded down and con bonus calculated separately (so I wouldn't have to worry about that)?