This work concerns a construction of pattern-avoiding inversion sequences from right to left we call the generating tree growing on the left. We first apply this construction to inversion sequences avoiding 201 and 210, resulting in a new way of computing their generating function. We then use a slightly modified construction to compute the generating function of inversion sequences avoiding 010 and 102, which was only conjectured before. These generating functions are algebraic in both instances. We end by discussing how the generating tree growing on the left can be applied in a more general setting.

23 pages, 3 figures, 1 table