Problem:
Score : 300 points

Problem Statement

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

Output

Print N lines. The i-th line should contain the value f(i).

Sample Input 1

20

Sample 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.

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;

namespace _20200711_A
{
    class Program
    {
        static void Main(string[] args)
        {
            //入力部
            int N;
            string input;
            int[] anser;

            input = System.Console.ReadLine();
            N = int.Parse(input);
            anser = new int[N + 1];
            for (int i = 0; i < N + 1; i++)
            {
                anser[i] = 0;
            }

            //計算部
            int ans = 0;
            for (int x = 1; x * x < N; x++)
            {
                for (int y = x; y * y < N; y++)
                {
                    for (int z = y; z * z < N; z++)
                    {
                        ans = x * x + y * y + z * z + x * y + y * z + z * x;
                        if (ans > N) continue;
                        if (x == y && y == z)
                        {
                            anser[ans]++;
                            continue;
                        }
                        if (x == y || y == z || z == x)
                        {
                            anser[ans] += 3;
                            continue;
                        }
                        anser[ans] += 6;
                    }
                }
            }
            //for(int i = 0; i < N; i++)
            //{
            //    if (!((i+1) % 2 == 1)) continue;
            //    if (!(a[i] % 2 == 1)) continue;
            //    anser++;
            //}


            //出力部
            for (int n = 1; n < N + 1; n++)
            {
                Console.WriteLine(anser[n].ToString());

            }

            input = System.Console.ReadLine();
        }
    }
}