  Let $\mathcal{T}_3$ be the three-rowed strip. Recently Regev conjectured that
the number of standard Young tableaux with $n-3$ entries in the "skew
three-rowed strip" $\mathcal{T}_3 / (2,1,0)$ is $m_{n-1}-m_{n-3}$, a difference
of two Motzkin numbers. This conjecture, together with hundreds of similar
identities, were derived automatically and proved rigorously by Zeilberger via
his powerful program and WZ method. It appears that each one is a linear
combination of Motzkin numbers with constant coefficients. In this paper we
will introduce a simple bijection between Motzkin paths and standard Young
tableaux with at most three rows. With this bijection we answer Zeilberger's
question affirmatively that there is a uniform way to construct bijective
proofs for all of those identites.
