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 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    //input
    int n = sc.nextInt();

    //output
    for(int m = 1; m <= n; m++){
      if( m < 6 ){
        System.out.println(0);
      }else{
        int count = 0;
        int zMax = 2;
        boolean zMaxCreated = false;
        for(int x = 1; x < 101; x++){
          if( x >= zMax ){
            break;
          }
          for(int y = 1; y < 101; y++){
            if( y >= zMax ){
              break;
            }
            double value = Math.pow(x,2)+Math.pow(y,2)+Math.pow(1,2)+(x*y)+(y*1)+(1*x);
            if( value > m ){
              if( !zMaxCreated ){
                zMax = 1;
                zMaxCreated = true;
              }
            }else{
              if( value == m ){
                count++;
              }
            }
            for(int z = 2; z < 101; z++){
              value += ((2*z)-1+y+x);
              if( value > m ){
                if( !zMaxCreated ){
                  zMax = z;
                  zMaxCreated = true;
                }
                break;
              }else{
                if( value == m ){
                  count++;
                }
              }
            }
          }
        }
        System.out.println(count);
      }
    }
  }
}