I am not a good reference but objective is important for repetitions. If you want better muscular development, stronger or more explosive, the number repetitions are different. First, you work chest and back or legs but never both, quadriceps are so big and ask a lot of energy. Pull-up, the day you work your arms.
If you goal is to increase number of pull-ups, this is more endurance.
Also, you have to do, your complete exercise, many muscles working in a pull-up, with 6 repetitions and then you go to workout arms with dumbbells and barebells for your triceps and chest. You start with a long and light series to keep muscles warm, you increase near your maximum with 12 repetitions, increase 1 kg with 8 repetition and two other series of 4 repetitions with maximum load. This is useless to have weighted pull-ups to increase number.
Take care to not make the same mistake than me, movement is less important than the way you use your muscles. Also, if you cannot do that, you cheat the last. Moreover, wide pull-up looks bad and lowerbut that gives a muscular back.
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