I'll give it a shot, Drew!
OK, this has a ton of variables, a literal fog of possibilities so it is tough to give an accurate answer. Assuming you are talking HT, your center channel is around 95dB efficient and (just guessing) you have around 100 watts of power and sit back around 10 to 13 feet from the speakers (3 to 4 meters) Basically, you should be able to get "reference volume" or 105dB peaks at your sitting position. Reference volume to "match" that capability is 10dB higher at 115dB at your seated position. Yeah, there is math involved but also adjusted because you are in a typical smaller room (it is small compared to a nightclub or stadium!) Am I close so far?
Alright, to get that kind of performance, you will need some firepower! Sub bass is all about moving air or bore X stroke. This applies to traditional direct radiator type subs (sealed, ported or infinite baffle) Horn loaded or bandpass are different animals and those types tend towards building your own as they are quite huge, very heavy and complex devices. Sure, you can get tapped horn subs for theaters but you get the idea. Power applied to a subwoofer is but one factor, there are other factors that apply to actually making sound--speaker efficiency or how much sound energy the device can provide at one watt measured at one, or extrapolated down to one meter. Ported speakers tend to be more efficient or require less power than sealed to get the same SPL (look at pro sound speakers, they tend to be ported for that reason) Ported is far, far more efficient at their tuned frequency and as long as that frequency limit is good for you, tend to be the best choice if cost or quantity of subwoofers is a concern.
The other factor is you generaly need two subwoofers to get even bass response in more than one seat. (Don't shoot the messenger!) However, you might be able to get away with one as long as it is positioned correctly and you mentioned one seat--you might be able to get away with one sub if you do a "sub crawl" not hard to do but not really important right now (sub crawl can be searched on AVS or youtube for more information)
A word of warning, the AVS crew generally don't sit around and listen to folk music and sipping tea...just letting you know bass heads exist in the shadows of thease forums.
I have been accused but not (yet) convicted of such low frequencies crimes against automotive glass, drywall and waking the neighbors.
This can get really wordy, quite complex and so on...however, there is one saving grace. You can use more than one sub if your needs demand more even bass response (a full couch instead of a chair) if you demand more SPL because your needs change and so on. I offer this as "advice" get a 15 inch ported sub that offers multiple ports so you can change the tuning or try sealed if you like. I know that Hsu and SVS offers those--they are not inexpensive but if cost is tight right now, a 12 would give you something as long as it can be tuned to around 20Hz or lower. You can add a second one later...or a third...or a forth because this is AVS. Very broadly speaking, for most people in rooms your size a pair of 15's do the duty at quite high levels but not always! One guy on hear has over 30 subs soooo... To start, I'd look for a 12 or 15 inch sub that can run sealed or ported and try the low ported frequency to learn and hear what it will do for you. (Usually done by plugging one of the port) if you want more output, you can keep all the ports open for maximum output but it won't go as low. Plug all the ports for sealed operation and you can learn/understand how sealed works in your room.
Final answer? Sure, a 12 or 15 ported/sealed sub with the port plugs is the most flexible subwoofer alignment and you could add more to boost SPL and improve bass response across mutliple seats. If you catch the disease, even with a 12 incher running four of them with one in each corner should provide 95 percent of most peoples needs. If you are the type that likes "rockstar volume" or wants to duplicate a THX/Dolby theater sound in your house, I'd lean towards the 15 to start or start sniffing around at 18's. If you are the type to turn the bass up until the drywall cracks--then back it off a click or two--there is always DIY with stadium amps.
Hope that helps, you can't have "too much sub" because the lower in SPL, the lower your distortion will be which is always a good thing. Good luck and I hope I added more clarity than confusion.