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.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		sc.close();

		int end = 100;
		for(int i=1;i<=n;i++) {
			int ans =0;
			for(int x=1;x<=end;x++) {
				for(int y=x;y<=end;y++) {
					for(int z=y;z<=end;z++) {
						if((x+y+z)*(x+y+z)-(x*y+y*z+z*x)==i) {
							if(x==y&&y==z&&z==x) {
								ans++;
							}else if((x==y)||(y==z)||(y==z)) {
								ans = ans + 3;
							}else {
								ans = ans + 6;
							}
						}
						if((x+y+z)*(x+y+z)-(x*y+y*z+z*x)>=i) {
							break;
						}
					}
				}
			}
			System.out.println(ans);
		}
	}
}