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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
public class Main{
  public static void main(String[] args){
  	Scanner sc=new Scanner(System.in);
    int N = sc.nextInt();
    int a[]=new int[10001];
    int b[]=new int[10001];
    int c[]=new int[10001];
    
    for(int x=1;x<100;x++){
      for(int y=x;y<100;y++){
        for(int z=y;z<100;z++){
          int answer=((x+y)*(x+y)+(y+z)*(y+z)+(z+x)*(z+x))/2;
          if(answer<10001){
          	if(x==y&&y==z) a[answer]++;
          	else if(x==y||y==z) b[answer]++;
          	else c[answer]++;
          }
        }
      }
     }
     
     for(int i=1;i<=N;i++){
       System.out.println(a[i]+b[i]*3+c[i]*6);
     }
    
  }
}