{"status": "success", "data": {"description_md": "**POTD September 16, 2024**\n\nLet $\\mathcal{S}$ be the set of all finite sequences of positive integers $a_1, a_2, a_3, \\ldots, a_n$ such that $|a_k-a_{k-1}| = a_{k-2}$ for all $3 \\le k \\le n$. If $a_1 = a_2 = 1$ and $n = 18$, compute $|\\mathcal{S}|$.", "description_html": "<p><strong>POTD September 16, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">\\mathcal{S}</span> be the set of all finite sequences of positive integers <span class=\"katex--inline\">a_1, a_2, a_3, \\ldots, a_n</span> such that <span class=\"katex--inline\">|a_k-a_{k-1}| = a_{k-2}</span> for all <span class=\"katex--inline\">3 \\le k \\le n</span>. If <span class=\"katex--inline\">a_1 = a_2 = 1</span> and <span class=\"katex--inline\">n = 18</span>, compute <span class=\"katex--inline\">|\\mathcal{S}|</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #275", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}