Grand Motzkin paths and $\{0,1,2\}$-trees -- a simple bijection

Abstract

A well-known bijection between Motzkin paths and ordered trees with outdegree always $\le 2$, is lifted to Grand Motzkin paths (the nonnegativity is dropped) and an ordered list of an odd number of such $\{0,1,2\}$ trees. This offers an alternative to a recent paper by Rocha and Pereira Spreafico.