I was the most recent instructor of 61A and just wrote up tips on auditing it:
http://blog.pamelafox.org/2022/07/how-to-audit-cs61a.html
However, I don't recommend 61A for folks new to programming, it's better as a second course.
I don't remember if there were suggestions (like factorial for recursion or a summation formula for induction).
At that time it was taught by Brian Harvey. I liked him a ton. I know there have been other excellent 61A teachers, too.
If there's a kind of instruction that reliably teaches students as a whole to write recursive functions successfully in just an hour, that will be a great advance for computer science education.