Cool!

The first thing I'd suggest would be to find a progression that's a lot harder. 20 reps of any exercise will build strength but it will mostly build what's known as strength endurance and not raw strength. If you are having trouble with pullups you need all the raw strength you can get to get your first one, the strength endurance can come later.

Something you can do less than 6 reps of would be great and then do just 3 sets of 3-5 good reps. Australian pullups are good start for many people but if they are too hard you might have to find a way to assist them either with a training partner or bands ect.

Then when you can do 6 or more reps, move on to full pullup negatives and just do 3 sets of 2 or 3 reps, So jump to the top or use a chair or a box to get into the top position and fall down as slowly and controlled as you can, again just do two or three sets. After about two weeks of doing negatives start adding a few static holds during the negative rep, stop and hold near the top, about half way down and just before the bottom when your arms are still slightly flexed.

Still do a set or two of Australian pullups after you train the negatives, but don't feel the need to get a pump or burn, it's just not needed and counter productive.

This is fairly standard strength training advice. It's based on how our muscles produce energy. For a full power contraction our muscles use the phosphate energy pathways (ATP) and that system works for about 8 seconds before other energy systems (hydrogen buffering etc) come into play to keep our muscles going at a lower output rate.

That's why the reps need to be kept low and fairly heavy if you want to maximize strength gains - typically 6 or less for all out strength and around 80% or your maximum potential (1RM) give or take a few percent.

Our phosphate energy system works at it's peak for roughly 8 seconds and then rapidly tapers off in the first set and then in subsequent sets it stops a bit quicker, so maybe 7, 6, or 5 seconds depending on how tough the effort applied is.

So to get strong try take maximum advantage of the phosphate energy system and keep your reps low and your time under tension (TUT) for the set under 8 seconds.

Test yourself for a full pullup from time to time and you might find one day you can just do one.

This advice is not set in stone, so feel free to adapt it in any way you feel will give you the most benefit. You may want to skip the Australian pullups completely or even skip the negatives and just go straight to band assisted pullups that you can do with a bit of discomfort in the 3-6 rep range and that will get you there too.

Find the best progressions that you can adapt to to your training and keep the reps low and fairly tough and you will get there. I promise!