First of all, 20 pullups is quite a feat, good job! I assume you are doing them with proper form: chin over bar on top, elbows locked and body still at the bottom. If you are doing something else, or eg. kipping pullups (basically, using your momentum in any way), the first thing you should do is transition to strict form pullups.
Doing 50 pullups is as much a matter of endurance as it is of strength. Personally, I've had a lot of good results doing weighted pullups, which build up strength. This will allow you to literally "fly" once the weight is off. What you want to do is to use a dip-belt and hang progressively bigger weights on it. You could also use a backpack (and fill it with eg. bags of sand) but it tends to hang awkwardly and it messes up your center of mass; because of this it also limits the amount of weight you can add. Using a dip belt takes care of all this. You should start low, a few kilograms added only (so as not to stress your joints too much). You should be able to add about 2 or 2.5 kgs every week. You can combine weighted pullups with any sort of program.
As for the program itself, I've again had a lot of luck doing "ladders". Basically, do 1, then 2, then 3 up to as much as you can, and then all the way back. Add a final "max effort" series at the end. If the last series is close or above your maximum, increase the max next time. The idea is to completely slaughter yourself. Doing ladders is beneficial because it will help with both strength (low reps, especially on the way back) and endurance (the high reps).
All that said, though, I don't think I know anyone who can do 50 strict form pullups, so this is all purely academic. Also, when you say you can do over a hundred with pauses, is this with hanging all the time or with letting go of the bar? If you are hanging through all this, then you are way beyond me and this advice might not apply to you at all.
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Bonus: Most people will find chin-ups easiest (with mixed grip in the middle and pullups the hardest) but this depends on how well some specific muscles are developed and even your technique. They all target slightly different muscle groups, though, so for the best overall results you should probably try to use all grips (and even vary your grip width). If you must focus on one, the most popular choice are pullups.
