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 (Python):
from math import sqrt
import sys
sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline

N = int(input())

def solv_quadratic_equation(a, b, c):
    D2 = b**2 - 4*a*c
    if D2<0:
        return 0.1, 0.1
    D = sqrt(D2)
    x_1 = (-b + D) / (2 * a)
    x_2 = (-b - D) / (2 * a)

    return x_1, x_2

for n in range(1,N+1):
    ans=0
    if n < 6:
        print(0)
        continue
    for x in range(1,int(sqrt(n-3))+1):
        for y in range(1,int(sqrt(n-3))+1):
            z1,z2=solv_quadratic_equation(1,x+y, x**2+y**2+x*y-n)
            if z1.is_integer() and z1>=1:
                ans+=1
            if z2.is_integer() and z2>=1:
                ans+=1

    print(ans)

Solution (Python):
n=int(input())
A=[0]*n
for i in range(3,int(n**0.5+150)):
  for j in range(1,i-1):
    for k in range(1,i-j):
      if (x:=i*i-j*k-k*(l:=i-j-k)-l*j)<=n:
        A[x-1]+=1
for a in A:
  print(a)

Solution (Python):
N = int(input())
List = [0]*N
for a in range(1, int(N**.5)+1):
  for b in range(1, int(N**.5)+1):
    M = a+b
    T = a**2+b**2+a*b+M+1
    c = 3
    while T<=N:
      List[T-1] += 1
      T = T+M+c
      c += 2
for l in List:
  print(l)