Hehehe...this is always a fun topic.
Let's start with some math.
The best AC units out there will do slightly better than 100 watts of draw per 1000 BTU's of cooling while the vast majority will draw more than 100 watts, but that is a decent starting point just for the sake of argument.
So...100 watts per 1000 BTU's with one 13,500 BTU roof unit...that's 1350 watts. Easy enough, right?
1350 watts=12 volts * X amps which leads us to 112.50 amps of draw on the 12 volt battery/alternator side of things.
Amp hours are a measure of a battery's storage capacity and are quite simply that...amps times hours. 1 amp for 5 hours is 5 amp hours. 5 amps for 1 hour is 5 amp hours. Now there is more to it thanks to this guy named Peurket, but that is bad news for you so we'll leave that out of this discussion.
In a typical day lets say you have the AC unit running at full bore for 8 of the 24 hours.
8 hours * 112.50 amps= 900 amp hours
Since you want to be able to run for three days we will multiply that figure by 3 so we get 2700 amp hours of battery capacity needed to run the AC unit (and only the AC unit) for 3 days like you planned on. Good to this point?
Deep cycle batteries are rated in amp hours just like we've converted the load into making it simple to see how much battery power you need. There's lots to it, but basically you want twice as much capacity in the battery as you're going to use to maximize its life. So if you need 200 amp hours for a day you should plan a bank with a total capacity of 400 amp hours.
Golf cart batteries are far and away the most economical route when you break it down to dollars per amp hour. They are also quite resilient. 8D's are also good, but for the sake of argument we're going to give you all the advantage we can so we're sticking to golf cart batteries.
Deka is a well known brand in the battery business. Their GC25 is the highest capacity Group GC2 battery they make with a rating of 225 amp hours (ignoring that Peukert guy again). Lead prices are extremely volatile, but I'm going to price that one at $100 estimating from what I know.
Ok...225 amp hours...but that's at 6 volts. We need two of them connected in series to get 12 volts to be usable by the inverter. So...$200 for 225 amp hours. We needed how many amp hours? Oh yeah...2700 for the three day weekend.
12*2 to get 12 volts=24
Hmmm...24 batteries at $100 each means $2400 worth of batteries alone JUST for the AC while ignoring lots of other important stuff (like the Peukert fellow). But that's not it...we need to DOUBLE the bank so that our depth of discharge is only 50%.
$4800 worth of batteries weighing about 70 lbs each (3360 total weight) JUST for the AC. Uh oh...
Check out the thread entitled "Jacuzzi Bus 4" and look at what Jason is doing to power his AC off an alternator going down the road. While parked he will use his gen-set or shore power no doubt.
I don't mean to rain on your parade, but coping with living off batteries is something we all must go through. For now we all have had to deal with a gen-set, deal with the heat, or always stay at a place with a plug in if we want AC. If you can come up with a more glamorous solution I PROMISE you will be everyone's favorite, but for now I think you might want to rethink what you want and need.