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 Python (3.8.2) (judge verdict: Accepted)

import math
n = int(input())

def f(x,y,z):
  return x**2 + y**2 + z**2 + z*x + x*y + y*z

current = [1,1,1]
ans = 0
p = [0 for _ in range(n+1)]
m = math.ceil(math.sqrt(n))+1
for i in range(1, m):
  f_ = f(i, 1, 1)
  if f_ > n:
    break
  for j in range(1, m):
    f_ = f(i,j,1)
    if f_ > n:
      break
    for k in range(1, m):
      f_ = f(i,j,k)
      if f_ > n:
        break
      p[f_] += 1
for i in range(1, n+1):
  print(p[i])