A note on triangular derivations of $\mathbf{k}[X_1,X_2,X_3,X_4]$

For a field $\mathbf{k}$ of characteristic zero, and for each integer $n\geq 4$, we construct a triangular derivation of $\mathbf{k} [X_1,X_2,X_3,X_4]$ whose ring of constants, though finitely generated over $\mathbf{k}$, cannot be generated by fewer than $n$ elements.