2021 AMC 12A Problem 8

A sequence of numbers is defined by D_0=0,D_1=0,D_2=1 and D_n=D_{n-1}+D_{n-3} for n\ge 3. What are the parities (evenness or oddness) of the triple of numbers (D_{2021},D_{2022},D_{2023}), where E denotes even and O denotes odd?

\textbf{(A) }(O,E,O) \qquad \textbf{(B) }(E,E,O) \qquad \textbf{(C) }(E,O,E) \qquad \textbf{(D) }(O,O,E) \qquad \textbf{(E) }(O,O,O)

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.