  We shed light on the structure of the "three-operator" version of the
forward-Douglas--Rachford splitting algorithm for finding a zero of a sum of
maximally monotone operators $A + B + C$, where $B$ is cocoercive, involving
only the computation of $B$ and of the resolvent of $A$ and of $C$, separately.
We show that it is a straightforward extension of a fixed-point algorithm
proposed by us as a generalization of the forward-backward splitting algorithm,
initially designed for finding a zero of a sum of an arbitrary number of
maximally monotone operators $\sum_{i=1}^n A_i + B$, where $B$ is cocoercive,
involving only the computation of $B$ and of the resolvent of each $A_i$
separately. We argue that, the former is the "true" forward-Douglas--Rachford
splitting algorithm, in contrast to the initial use of this designation in the
literature. Then, we highlight the extension to an arbitrary number of
maximally monotone operators in the splitting, $\sum_{i=1}^{n} A_i + B + C$, in
a formulation admitting preconditioning operators. We finally demonstate
experimentally its interest in the context of nonsmooth convex optimization.
