{"status": "success", "data": {"description_md": "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?\n\n$\\textbf{(A) }(O,E,O) \\qquad \\textbf{(B) }(E,E,O) \\qquad \\textbf{(C) }(E,O,E) \\qquad \\textbf{(D) }(O,O,E) \\qquad \\textbf{(E) }(O,O,O)$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A sequence of numbers is defined by  <span class=\"katex--inline\">D_0=0,D_1=0,D_2=1</span>  and  <span class=\"katex--inline\">D_n=D_{n-1}+D_{n-3}</span>  for  <span class=\"katex--inline\">n\\ge 3</span> . What are the parities (evenness or oddness) of the triple of numbers  <span class=\"katex--inline\">(D_{2021},D_{2022},D_{2023})</span> , where  <span class=\"katex--inline\">E</span>  denotes even and  <span class=\"katex--inline\">O</span>  denotes odd?</p>&#10;<p> <span class=\"katex--inline\">\\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)</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2021 AMC 12A Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12A_p09", "prev": "/problem/21_amc12A_p07"}}