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.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        for(int i=1; i<=n; i++) {
            int ans = 0;
            for(int x=1; x<=1000; x++) {
                int x1 = (int) Math.pow(x, 2);
                int y1 = (int) Math.pow(1, 2);
                int z1 = (int) Math.pow(1, 2);
                int xy1 = x * 1;
                int yz1 = 1 * 1;
                int zx1 = 1 * x;
                int sum1 = x1 + y1 + z1 + xy1 + yz1 + zx1;
                if(i < sum1)break;
                for(int y=1; y<=1000; y++) {
                    int x2 = (int) Math.pow(x, 2);
                    int y2 = (int) Math.pow(y, 2);
                    int z2 = (int) Math.pow(1, 2);
                    int xy2 = x * y;
                    int yz2 = y * 1;
                    int zx2 = 1 * x;
                    int sum2 = x2 + y2 + z2 + xy2 + yz2 + zx2;
                    if(i < sum2)break;
                    for(int z=1; z<=1000; z++) {
                        int x3 = (int) Math.pow(x, 2);
                        int y3 = (int) Math.pow(y, 2);
                        int z3 = (int) Math.pow(z, 2);
                        int xy3 = x * y;
                        int yz3 = y * z;
                        int zx3 = z * x;
                        int sum3 = x3 + y3 + z3 + xy3 + yz3 + zx3;
                        if(i == sum3) ans++;
                        if(i < sum3)break;
                    }
                }
            }
            System.out.println(ans);
        }
    }
}