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 collections import defaultdict
n = int(input())
dic = defaultdict(int)
for i in range(1,100):
    for j in range(1,100):
        for k in range(1,100):
            dic[i**2+j**2+k**2+i*j+j*k+k*i] += 1

for i in range(1,n+1):
    print(dic[i])

Solution (Python):
n=int(input())

arr = [[[0 for _ in range(101)] for _ in range(101)] for _ in range(101)]

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

table = [0]*10001

for i in range(1,101):
    for j in range(1,101):
        for k in range(1,101):
            re = g(i,j,k)
            if re <= 10000:
                table[re]+= 1



for i in range(1,n+1):
    print(table[i])

Solution (Python):
import sys

input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)


def main():
    N = int(input())
    MAX = int(N ** 0.5)

    res = [0] * 10008

    ans = 0
    li = []
    for x in range(1, MAX + 1):
        for y in range(1, MAX + 1):
            for z in range(1, MAX + 1):
                tmp = x ** 2 + y ** 2 + z ** 2 + x * y + y * z + z * x
                if tmp <= 10000:
                    res[tmp] += 1

    for i in range(1, N + 1):
        print(res[i])


if __name__ == "__main__":
    main()

Solution (Python):
from math import sqrt
n = int(input())
l = [0]*(n)
s = int(sqrt(n))
for x in range(1, s+1):
  for y in range(1, s+1):
    for z in range(1, s+1):
      i = x**2+y**2+z**2+x*y+y*z+z*x
      if i-1 < n:
        l[i-1] += 1
        
for i in l:
  print(i)

Solution (Python):
n=int(input())
z=0
N=[0]*10000
ans=0
ko=0
for x in range(1,101):
    for y in range(1,101):
        for z in range(1,101):
            ko=x**2+y**2+z**2+x*y+y*z+z*x
            if ko<=n:
                N[ko-1]+=1
            else:
                break
for i in range(n):
    print(N[i])