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: Wrong Answer)

import java.util.*;

public class Main {
 
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        StringBuilder sb = new StringBuilder();
        for (int i = 1; i <= N; i++) {
            long count = 0;
            for (long a = 1; a <= Math.sqrt(i-3); a++) {
                for (long b = 1; b <= Math.sqrt(i-a*a-a-1); b++) {
                    long ans = i - a*a - b*b - a*b;
                    for (long c = (int)Math.sqrt(ans)-1; c < Math.sqrt(ans); c++) {
                        if (ans == c*c + a*c +b*c) {
                            count++;
                        }
                    }
                }
            }
            sb.append(count).append("\n");
        }
        System.out.println(sb);
    }
}