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 System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
class c{
    public static void Main(){
        //2StreamWriter sw = new StreamWriter("out.txt");
        int n = int.Parse(Console.ReadLine());
        int[] ans = new int[n+1];
        for(int x=1; x<=(int)Math.Sqrt(n); x++){
            for(int y=1; y<=(int)Math.Sqrt(n); y++){
                for(int z=1; z<=(int)Math.Sqrt(n); z++){
                    int t = (x*x)+(y*y)+(z*z)+(x*y)+(y*z)+(z*x);
                    if(t <= n){
                        ans[t]++;
                    }
                }
            }
        }
        for(int i=1; i<=n; i++){
            Console.WriteLine(ans[i]);
        }
    }
}