So, he rejected me BUT he still wants to hang out. Who should initiate hang outs then?

Anonymous
We weren't friends before so I really have no clue how to proceed with this. I want to hang out with him and just be friends because he's cool and I'm not the type that goes crazy after rejection. But I was never just friends after someone who rejected me or whom I rejected, this the first time I actually want to.
He rejected me a month ago so it's not that fresh and we hanged out couple of times after that. But I just realized that both times it was me initiating (prior to him texting me). I'm really okay with being just friends but I don't want to be that girl who he feels sorry for and now feels obligated to hang out with, just because he romantically rejected me. He always responds and is always in the good mood and he never said no to meeting up... but he hasn't really initiated it himself and this got me worried that he actually doesn't want to hang out. :/ Should I back off?
So, he rejected me BUT he still wants to hang out. Who should initiate hang outs then?
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