Unfortunately, I don't really understand how it works. Сould you help me here too? You could post the answer on the page of my other question: mathoverflow.net/questions/446148/….

Thank you again! If we change $(k+1)$ to $(k+2)$, we get A258173 as a result. The description provides a combinatorial interpretation through rooted trees. Does FindStat only work with permutations and binary words, or can we also get a result for this case?

Thank you for answer! Is it correct that FindStat automatically finds the desired sequence of transformations? Is it also correct that you set the length of transformations by yourself? If so, how do you know what the length should be? Also, could you look at this question: mathoverflow.net/questions/436336/…?

@PeterTaylor, thak you for comment! Could you write your own answer including the proof? In that case, I could delete my useless answer based on the experimental result.