XYZ Triplets

AtCoder

IDaising2020_c

Time2000ms

Memory256MB

Difficulty—

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 of $f(1),f(2),f(3),\ldots,f(N)$. ## Constraints * All values in input are integers. * $1 \leq N \leq 10^4$ ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

*   For $n=6$, only $(1,1,1)$ satisfies both of the conditions. Thus, $f(6) = 1$.
*   For $n=11$, three triples, $(1,1,2)$, $(1,2,1)$, and $(2,1,1)$, satisfy both of the conditions. Thus, $f(6) = 3$.
*   For $n=17$, three triples, $(1,2,2)$, $(2,1,2)$, and $(2,2,1)$, satisfy both of the conditions. Thus, $f(17) = 3$.
*   For $n=18$, three triples, $(1,1,3)$, $(1,3,1)$, and $(3,1,1)$, satisfy both of the conditions. Thus, $f(18) = 3$.

API Response (JSON)

{
  "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 o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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