{"problem":{"name":"XYZ Triplets","description":{"content":"Let $f(n)$ be the number of triples of integers $(x,y,z)$ that satisfy both of the following conditions: *   $1 \\leq x,y,z$ *   $x^2 + y^2 + z^2 + xy + yz + zx = n$ Given an integer $N$, find each o","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"aising2020_c"},"statements":[{"statement_type":"Markdown","content":"Let $f(n)$ be the number of triples of integers $(x,y,z)$ that satisfy both of the following conditions:\n\n*   $1 \\leq x,y,z$\n*   $x^2 + y^2 + z^2 + xy + yz + zx = n$\n\nGiven an integer $N$, find each of $f(1),f(2),f(3),\\ldots,f(N)$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 10^4$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"aising2020_c","tags":[],"sample_group":[["20","0\n0\n0\n0\n0\n1\n0\n0\n0\n0\n3\n0\n0\n0\n0\n0\n3\n3\n0\n0\n\n*   For $n=6$, only $(1,1,1)$ satisfies both of the conditions. Thus, $f(6) = 1$.\n*   For $n=11$, three triples, $(1,1,2)$, $(1,2,1)$, and $(2,1,1)$, satisfy both of the conditions. Thus, $f(6) = 3$.\n*   For $n=17$, three triples, $(1,2,2)$, $(2,1,2)$, and $(2,2,1)$, satisfy both of the conditions. Thus, $f(17) = 3$.\n*   For $n=18$, three triples, $(1,1,3)$, $(1,3,1)$, and $(3,1,1)$, satisfy both of the conditions. Thus, $f(18) = 3$."]],"created_at":"2026-03-03 11:01:14"}}