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):
n=int(input())
l=[0]*(10**4+1)
for x in range(1,100):
    for y in range(x,100):
        for z in range(y,100):
            t=x*x+y*y+z*z+x*y+y*z+z*x
            if t<=10**4:
                if (x!=y) and y!=z:
                    l[t]+=6
                elif x==y and y==z:
                    l[t]+=1
                else:
                    l[t]+=3
for i in range(1,n+1):
    print(l[i])

Solution (Python):
n = int(input())
for num in range(1,n+1):
    tmp = 0
    th = set([])
    for x in range(1,int(num**0.5)+1):
        for y in range(1,x+1):
            if (4*num-2*x*y-3*(x**2+y**2)) < 0:
                break
            z = ((4*num-2*x*y-3*(x**2+y**2))**0.5-(x+y))/2
            
            
            if z >= 1:
                if z.is_integer():
                    if x**2+y**2+z**2+x*y+y*z+z*x == num:
                        a = [x,y,z]
                        a.sort()
                        a = tuple(a)
                        if a not in th:
                            th.add(a)
                            if x==y and y==z:
                                
                                tmp += 1
                            elif x!=y and y!=z and z!=x:
                                
                                tmp += 6
                            else:
                                
                                tmp += 3
    print(tmp)

Solution (Python):
N = int(input())
arr = [0]*10002

def calc(x,y,z):
  ans = (x**2 + y**2 + z**2 + x*y + y*z + z*x) 
  return ans

for x in range(1,100):
  for y in range(1,100):
    for z in range(1,100):
        arr[min(calc(x,y,z),10001)] += 1
        
for i in range(1,N+1):
  print(arr[i])

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

a = [0]*(10**4)

for x in range(1,10**2):
    for y in range(1,10**2):
        for z in range(1,10**2):
            s = x**2 + y**2 + z**2 + x*y + y*z + z*x
            if s <= 10**4:
                a[s-1] += 1

for i in range(n):
    print(a[i])