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):

import collections

n_list = []

for x in range(1,100):
    for y in range(1,100):
        for z in range(1,100):
            n_list.append(x**2 + y**2 + z**2 + x*y + y*z + z*x)



N = collections.Counter(n_list)



for i in range(1,int(input())+1):
    
    try:
        print(N[i])
    except:
        print(0)

Solution (Python):
def m():
    N = int(input())
    M = 100
    dp = [[[0] for _ in range(M)] for _ in range(M)]
    ANS = [0] * (N+1)
    for i in range(1, M+1):
        for j in range(1, M+1):
            for k in range(1, M+1):
                a = pow(i,2) + pow(j,2) + pow(k,2)
                b = i*j + j*k + k*i
                tmp = a + b
                if tmp > N:
                    continue
                ANS[tmp] +=1
    for i in range(1, N+1):
        print(ANS[i])
m()

Solution (Python):
n = int(input())
ans = [0]*n

for x in range(1,100):
  for y in range(1,100):
    for z in range(1,100):
      tmp = x**2 + y**2 + z**2 + x*y + y*z + z*x
      if tmp <= n:
        ans[tmp-1] += 1

for nn in range(n):
  print(ans[nn])

Solution (Python):
def main():
    N= int(input())
    A = [0]*10**5
    for x in range(1,101):
        for y in range(1,101):
            for z in range(1,101):
                n = x*x + y*y + z*z + x*y + y*z + z*x 
                A[n] += 1
    for i in range(1,N+1):
        print(A[i])
if __name__ == '__main__':
    main()

Solution (Python):
N = int(input())
cnt = [0]*N
for x in range(1,100):
  for y in range(1,100):
    for z in range(1,100):
      s = x**2+y**2+z**2+x*y+y*z+z*x
      if s <= N:
        cnt[s-1] += 1     
for i in cnt:print(i)