To begin at the end since the consequences of a mistake given the "loose" information provided is death I would seek medical advise as to "What type" of altitude sickness you are experiencing. The last thing you want to do is have enough O2 to get you higher on the mountain and then run out.
That said there has been lots of sound advise on hydration, acclimatizing, and the use of aspirin to help your prep.
Now to the O2 tank question. I think you are going to find it more complex than your original thought. O2 tanks come in many sizes. The largest size aluminum tank I could reasonably imagine in a backpack would be a "D". If your "train" comes off the track at 13K then you'll need 6-10 liter flow or to begin with a lesser flow at a lower altitude. At a 6 liter flow a "D" tank would have 42 mins of O2. That's 21 mins to cover you last 1000'-1200', tag the summit and 21 mins to descend back to 13K.
Those tanks weigh 5.5lbs empty. At 1000' per hour that would be close to 20 lbs of O2 and tanks. If you required a 10 liter flow then double you tanks or cut your time in half. (I'll get to what happens when you drop one later)
"Increase the time = decrease the amount of O2" "Increase the amount of O2 = decrease the time you breath O2 with the possibility of stranding you much higher than 13K with no supplemental oxygen and 10-20 extra pounds of empty O2 bottles.
Drop a tank the wrong way and it turns into a missile powerful enough to go through a brick wall. Composite O2 Tanks are $500 plus empty and are more delicate.
If you go the O2 route I suggest a mask from http://www.topout.co.uk
If you don't have a schedule to "get" to altitude to condition your "Blood" then bring it to you. This system is not cheap but it's not a waste of time either if you are training for altitude.http://altolab-usa.com
Good luck whatever you decide