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: Runtime Error)

import java.util.*;
import java.io.*;

public class Main {
  static int len;

  // sum of divisor
  public static void main(String[] args) throws IOException {
    sc = new MScanner(System.in);
    pw = new PrintWriter(System.out);
    int n = sc.nextInt();
    int[] res = new int[n];
    int th = (int) Math.floor(Math.sqrt(n));
    for (int x = 1; x <= th; x++) {
      for (int y = 1; y <= th; y++) {
        for (int z = 1; z <= th; z++) {
          int k = (int) Math.pow(x + y + z, 2) - x * y - y * z - x * z;
          if (k >= 0 && k <= n + 1) {
            res[k - 1]++;
          }
        }
      }
    }

    pw.println(Arrays.toString(res));
    pw.flush();

    // sc.close();
    // pw.println(cnt);
    // pw.flush();
  }

  private static boolean isPrime(int num) {
    for (int i = 2; i < num; i++) {
      if (num % i == 0) {
        return false;
      }
    }
    return true;
  }

  static PrintWriter pw;
  static MScanner sc;

  static class MScanner {
    StringTokenizer st;
    BufferedReader br;

    public MScanner(InputStream system) {
      br = new BufferedReader(new InputStreamReader(system));
    }

    public MScanner(String file) throws Exception {
      br = new BufferedReader(new FileReader(file));
    }

    public String next() throws IOException {
      while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
      return st.nextToken();
    }

    public int[] intArr(int n) throws IOException {
      int[] in = new int[n];
      for (int i = 0; i < n; i++) in[i] = nextInt();
      return in;
    }

    public long[] longArr(int n) throws IOException {
      long[] in = new long[n];
      for (int i = 0; i < n; i++) in[i] = nextLong();
      return in;
    }

    public int[] intSortedArr(int n) throws IOException {
      int[] in = new int[n];
      for (int i = 0; i < n; i++) in[i] = nextInt();
      shuffle(in);
      Arrays.sort(in);
      return in;
    }

    public long[] longSortedArr(int n) throws IOException {
      long[] in = new long[n];
      for (int i = 0; i < n; i++) in[i] = nextLong();
      shuffle(in);
      Arrays.sort(in);
      return in;
    }

    public Integer[] IntegerArr(int n) throws IOException {
      Integer[] in = new Integer[n];
      for (int i = 0; i < n; i++) in[i] = nextInt();
      return in;
    }

    public Long[] LongArr(int n) throws IOException {
      Long[] in = new Long[n];
      for (int i = 0; i < n; i++) in[i] = nextLong();
      return in;
    }

    public String nextLine() throws IOException {
      return br.readLine();
    }

    public int nextInt() throws IOException {
      return Integer.parseInt(next());
    }

    public double nextDouble() throws IOException {
      return Double.parseDouble(next());
    }

    public char nextChar() throws IOException {
      return next().charAt(0);
    }

    public long nextLong() throws IOException {
      return Long.parseLong(next());
    }

    public boolean ready() throws IOException {
      return br.ready();
    }

    public void waitForInput() throws InterruptedException {
      Thread.sleep(3000);
    }
  }

  static void shuffle(int[] in) {
    for (int i = 0; i < in.length; i++) {
      int idx = (int) (Math.random() * in.length);
      int tmp = in[i];
      in[i] = in[idx];
      in[idx] = tmp;
    }
  }

  static void shuffle(long[] in) {
    for (int i = 0; i < in.length; i++) {
      int idx = (int) (Math.random() * in.length);
      long tmp = in[i];
      in[i] = in[idx];
      in[idx] = tmp;
    }
  }
}