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: Time Limit Exceeded)

import java.util.*;
public class Main {

    static int[] f = null;

    static int rhs(int a, int b, int c){
        return ((a*a)+(b*b)+(c*c)+(a*b)+(b*c)+(a*c));
    }

    static void solve(){
        Scanner sc = new Scanner(System.in);
        int NOC = sc.nextInt(); 
        int n = NOC;
        f = new int[NOC];
        Arrays.fill(f,0);
        while(NOC-->0){
            int no = NOC+1;
            int max = (int)Math.ceil(Math.sqrt(n/3.0));
            int count = 0; 
            // Can we do better? I dont know..
            for(int i=1; i<=max;i++){
                for(int j=1; j<=max; j++){
                    for(int k=1; k<=max; k++){
                        int val = rhs(i,j,k);
                        if(val>no) break;
                        else if(val==no) count++;
                    }
                }
            }
            f[NOC]=count;
        }
        for(int a: f) System.out.println(a);
        sc.close();
    }
    
    public static void main(String args[]) {
        solve();
    }
}