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: Wrong Answer)

import itertools
n = int(input())
N = 1
while N**2 < n:
    N += 1
if N ** 2 > n: N-=1
ans = [0] * n

for x,y,z in itertools.combinations_with_replacement(list(range(1,N+1)), 3):
    a = x**2+y**2+z**2 + x*y+y*z+z*x
    if a > n: continue
    if x==y==z: b = 1
    elif x==y or x==z or y==z: b = 3
    elif x!=y and y!=z and x!=z: b = 6
    ans[a-1] = b
for i in ans: print(i)