Someone else correct me if I am wrong but isn't the rule of thumb to multiply the amps by the hours you need. I think the 100-240v 1.3amp can be ruled out as thats on the mains side of the powerbrick. Its the output of 4.7 amps thats the figure we need....I think.
BTW you would be best getting one of those Airtravel laptop 19v power bricks to suit your laptop which connects to 12v power sources with a cigaretted type plug, saves the conversion losses using an invertor converting from 12v to mains voltage for your current powerbrick that is converting it back to 12/19v again for the laptop anyway. Invertors waste a huge amount of battery energy.
Anyway 4.7 amps x 15 hours = 70ah
I don't know whether that formula takes into account the need not to drain a battery completely though I do understand that Deep cycle batteries are much better at handling significant drainage.
Probably best to be safe with a 100ah Deep Cycle.
Oh and get one with a built in extendable handlebar and wheels. Your back will thank you!
NB* Wait for more replies, I am no expert!! Just going on what I have read, or think I remember reading