The invention relates to the alfalfa variety designated R413A316. Provided by the invention are the seeds, plants and derivatives of the alfalfa variety R413A316. Also provided by the invention are tissue cultures of the alfalfa variety R413A316 and the plants regenerated therefrom. Still further provided by the invention are methods for producing alfalfa plants by crossing the alfalfa variety R413A316 with itself or another alfalfa variety and plants produced by such methods.