In the DMG (288-289) there is an optional rule for spell points, but warlocks are not mentioned.
Can warlocks use spell points for their magic?
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There's no point to doing this. The idea behind spell points is to have a single resource fueling your spells regardless of their level. However, Warlocks already have that, because their spell slots are only of a single level.
With that said, if you insist on doing this, the correct progression would be:
This is a direct translation of the Warlock's spell slots at each level into spell points; which is exactly how spell points are calculated for all other classes.
Note that if you use this system and allow the Warlock to create lower level spell slots than their maximum, you are fundamentally changing the Warlock class. I would carefully consider balance before I did this. Of course, if you don't allow them to create lower level spell slots, there is absolutely no point using the spell point system, since it will just be a direct translation of their spell slots.