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[n+1];
        for (int i = 1; i <= n; i++) {
            int t1 = i*i;
            if(n < t1)break;
            for (int j = 1; j <= n; j++) {
                int t2 = j*j + i*j + t1;
                if(n < t2)break;
                for (int k = 1; k <= n; k++) {
                    int t3 = k*k + i*k + j*k + t2;
                    if(n < t3)break;
                    a[t3]++;
                }
            }
        }
        StringBuilder sb = new StringBuilder();
        for (int i = 1; i <= n; i++) {
            sb.append(a[i] + "\n");
        }
        System.out.print(sb.toString());
        sc.close();

    }

}