The solution is so simple, I can't believe no one has figured it out.
First of all, it's idiotic to have him pay 0. Part of your electric bill, etc., is just associated with it being turned on. Your cable bill is the same, regardless of whether or not you watched television. So here's what I suggest:
Figure out your average monthly utility bill, or what it would have been for the month had he been present. Divide by 4. This is the amount that everyone is generally obligated to pay. Now, take that month's utilities, subtract 3 times the usual monthly payment for utilities, and he pays what's left.
i.e. if your utilities normally cost $500 for the month, that's $125 each.
If the month he was gone your utilities dropped to $460, then after each of the 3 of you using those utilities pay your $125, that leaves $85 for him to cover.