Recursive hierarchical embedding allows humans to generate multiple hierarchical levels using simple rules. We can acquire recursion from exposure to linguistic and visual examples, but only develop the ability to understand "multiple-level" structures like "[[second] red] ball]" after mastering "same-level" conjunctions like "[second] and [red] ball." Whether we can also learn recursion in motor production remains unexplored. Here, we tested 40 adults' ability to learn and generate sequences of finger movements using "multiple-level" recursion and "same-level" iteration rules (like linguistic conjunction). Rule order was counterbalanced. First, they learned the generative rules (without explicit rule instructions or feedback) by executing examples of motor sequences based on visual cues displayed on the screen (learning). Second, participants were asked to discriminate between correct and incorrect motor sequences beyond those to which they were previously exposed (discrimination). Finally, they were asked to use the rules to generate new hierarchical levels consistent with the previously given (generation). We repeated the procedure (all three phases) on 2 days, allowing for a night of sleep. We found that most participants could discriminate correct/incorrect sequences based on recursive rules and use recursive rules to generate new hierarchical levels in motor sequences, but mostly on the second day of testing, and when they had acquired iterative before recursive rules. This aligns with previous literature on vision and language and with literature showing that sleep is necessary to generate abstract knowledge of motor sequences. Lastly, we found that the ability to discriminate well-formed motor sequences using recursion was insufficient for motor generativity.