I'm going to guess that the power consumption for the concentrator is rated in Watts, not amps. Watts is a constant measurement regardless of voltage. Amps depends HEAVILY on voltage. Just doing a quick search, I found a "portable" Invacare concentrator that's rated for 280 watts at 3LPM, on 120v A/C (wall) power.
I'd recommend you buy an inverter that is rated for at least 50% more watts than the concentrator will draw. That will ensure it isn't operating at it's max all the time, and a 2x "surge" rating should ensure adequate ability to start the machine, which sometimes takes double or more the steady state power. A 400 watt inverter should be sufficient, and will draw about 22 amps from your vehicle to make 280 watts of 120V. (280W/13V=22A) (The inverter will see ~13v most of the time from your vehicle as long as it's running.)
22 amps of draw means you won't be able to use the cigarette lighter for two reasons: 1: Most are fused at 15A, and 2: An ordinary cigarette lighter plug will begin to get pretty warm over about 15A, and pulling over 20 may melt some of them. You'll really want to hard wire the inverter. I'd recommend using 10 ga wire to keep voltage drop to a minimum, and put a 40-50A circuit breaker or fuse as close to the battery as possible. Connect BOTH the power and ground leads directly to the battery, not to some other source of voltage, unless your car has one of the large 12v taps fed by a large size battery cable, often covered by a red cap. That would also be OK for getting power.
This is the breaker I'm talking about. I just bought a few of these off Ebay for a solar setup, and they work great!
http://www.ebay.com/itm/INLINE-AUTO-WATERPROOF-40-AMP-CIRCUIT-BREAKER-MANUAL-RESET-SWITCH-12VOLT-4-8-AWG-/271244959834
If you overload them, you just reset them, and you can use them to switch the power off as well. If you use 10ga "Zip" wire, it has power and ground already run together. Like this:
http://www.ebay.com/itm/10-Ft-10-GA-Gauge-Red-Black-Stranded-2-Conductor-Speaker-POWER-GROUND-WIRE-/161156437856?pt=LH_DefaultDomain_0&hash=item2585ac1760
Finally, as stated above, with a continuous draw of 20A, you'll probably want to leave the vehicle running as long as the concentrator is plugged in. Shutting it off for 20 minutes is probably OK if your battery is good, but longer periods may be at risk of not starting. (Ideally, a 20A load would drain a normal car battery to 50% in about 2 hours, but it's likely your battery isn't starting at 100%, and doesn't have as much reserve capacity as it is rated for anyway... If you really want to know how to figure out how long you can safely leave it with the engine off, PM me and I'll explain it. It doesn't sound like that's a concern though.
Chris