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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

using static System.Math;
using static System.Console;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System;

namespace AtCoder
{
    class Program
    {
        private static long mod = 1000000007;
        static void Main(string[] args)
        {
            var n = long.Parse(ReadLine());
            //var line = ReadLine().Split(' ').Select(value => long.Parse(value)).ToArray();

            var sqrt = (int)Sqrt(n);

            var dictionary = new Dictionary<int, int>();
            for(var i = 1; i <= sqrt; i++)
            {
                for(var j = 1; j <= sqrt; j++)
                {
                    for(var k = 1; k < sqrt; k++)
                    {
                        var value = i * i + j * j + k * k + i * j + j * k + i * k;
                        if (!dictionary.ContainsKey(value))
                        {
                            dictionary.Add(value, 0);
                        }
                        dictionary[value]++;
                    }
                }
            }

            for(var i = 1; i <= n; i++)
            {
                if(dictionary.ContainsKey(i))
                {
                    WriteLine(dictionary[i]);
                }
                else
                {
                    WriteLine(0);
                }
            }
        }
    }
}