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) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int count=0;

//		for(int i=1 ; i<=n ; i++) {
//			for(int x=1; x<=n ; x++) {
//				for(int y=1 ; y<=n ; y++) {
//					for(int z=1 ; z<=n ; z++) {
//						if(x*x + y*y + z*z + x*y + y*z + z*x == i) {
//							count++;
//						}
//					}
//				}
//			}
//			System.out.println(count);
//			count = 0;
//		}

		for(int i=1 ; i<=n ; i++) {
			for(int x=1; x<=n ; x++) {
				for(int y=1 ; y<=n - x*x; y++) {
					for(int z=1 ; z<=n - x*x - y*y - x*y ; z++) {
						if(x*x + y*y + z*z + x*y + y*z + z*x == i) {
							count++;
						}
					}
				}
			}
			System.out.println(count);
			count = 0;
		}

		scanner.close();

	}

}