The Lin–Ma conjecture on 0012-avoiding inversion sequences

An inversion sequence of length $n$ is a sequence $e=e_1e_2\cdots e_n$ such that $0\le e_i\le i-1$ for $1\le i\le n$; let $\mathbf{I}_n(0012)$ denote the set of inversion sequences of length $n$ avoiding the pattern $0012$. Lin–Ma conjecture. For every $n\ge 1$,

$$|\mathbf{I}_n(0012)|=1+\sum_{i=1}^{n-1}\binom{2i}{i-1}.$$

This conjecture concerns the enumeration of inversion sequences avoiding a fixed pattern. The paper's abstract says that the authors confirm the conjecture and also obtain a formula for the subclass in which the last entry equals $n-1$, so the conjecture is solved.