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())

ls = [
    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6,0,12,36,78,36,42,0,36,0,78,24,48,24,18,30,90,15,96,18,27,21,54,0,24,21,48,27,84,18,48,42,36,6,66,12,108,12,42,0,48,9,27,60,21,36,84,6,36,18,42,18,54,18,60,0,60,15,72,9,99,42,12,12,60,0,57,42,18,18,78,0,42,6,36,36,63,9,42,15,30,18,78,6,24,48,42,0,102,12,75,45,42,30,84,24,66,9,24,30,90,24,42,0,24,3,84,21,84,33,66,24,36,6,36,48,51,18,72,0,66,18,54,30,24,18,48,18,30,0,102,12,45,36,24,0,102,3,42,15,42,54,54,21,66,24,66,30,102,3,66,0,48,12,24,30,45,36,54,6,78,9,48,24,39,36,96,0,66,6,27,27,60,30,18,30,48,12,90,24,60,36,6,0,42,12,78,36,36,24,114,6,60,0,18,6,69,18,84,0,36,6,48,6,39,24,42,24,54,6,72,48,36,42,60,0,48,0,36,18,138,24,30,30,42,18,75,18,48,18,24,0,78,0,78,57,60,9,48,9,36,30,30,42,42,39,84,0,24,12,87,27,30,42,24,24,90,0,36,24,60,36,84,0,42,0,30,21,87,12,72,24,42,12,60,30,72,21,60,0,96,12,30,42,39,18,66,12,84,12,63,42,42,24,42,0,18,6,78,15,75,45,54,12,54,6,84,30,30,18,54,0,42,24,39,27,96,18,42,21,48,0,54,18,33,36,66,0,84,0,75,48,30,42,54,12,54,15,42,30,96,18,42,0,18,6,123,15,48,24,48,39,42,6,21,54,45,12,60,0,90,12,30,36,45,18,72,21,78,12,30,12,60,30,18,0,78,6,60,36,33,18,60,12,30,0,60,18,90,30,54,0,36,1,78,27,84,30,18,15,102,9,27,30,24,57,90,0,42,9,48,42,42,12,72,27,48,9,108,18,48,48,18,0,84,6,66,24,48,21,114,6,78,24,30,30,42,18,60,0,18,12,63,9,51,66,48,15,54,0,66,60,36,18,48,0,66,6,36,30,96,9,36,30,30,24,93,24,72,24,66,0,60,24,48,30,24,30,72,6,60,12,30,12,93,18,72,0,30,0,81,30,36,48,36,30,90,6,54,24,57,24,36,0,54,18,36,24,78,18,72,33,12,0,51,30,48,24,42,0,90,3,78,30,30,27,138,6,30,18,36,24,75,24,12,0,54,12,42,18,84,36,30,18,66,6,45,36,36,48,114,0,24,6,30,21,108,15,48,18,36,18,57,24,63,42,54,0,78,6,81,36,18,24,42,18,120,0,24,24,66,12,54,0,48,12,66,18,42,36,48,18,72,6,48,48,33,6,102,0,54,24,39,54,60,12,90,18,36,3,111,24,51,48,42,0,90,0,45,36,54,48,54,24,18,18,51,18,72,0,54,0,18,12,54,36,57,18,42,18,120,0,63,42,27,36,48,0,54,6,39,30,81,18,72,33,54,9,72,12,54,54,24,0,54,15,75,24,60,12,78,6,30,12,39,54,72,6,54,0,72,6,78,12,54,39,30,15,48,6,57,48,18,24,90,0,90,18,42,24,39,42,24,30,42,0,84,6,66,30,30,0,30,0,27,42,39,33,90,24,84,18,51,36,69,24,54,0,42,18,87,33,51,18,42,9,126,9,84,36,66,18,54,0,36,0,66,12,48,15,54,30,18,18,60,18,96,54,42,0,102,0,27,36,30,36,108,15,54,0,24,36,60,24,66,0,30,0,54,15,75,48,36,18,48,24,36,36,54,15,108,0,84,18,
]

for i in range(N):
    print(ls[i])

Solution (Python):
lst=[0 for i in range(10000)]
for x in range(1,102):
    for y in range(1,101):
        for z in range(1,101):
            a=x**2+y**2+z**2+x*y+y*z+z*x
            if a<10001:
                lst[a-1]+=1
n=int(input())
for i in range(n):
    print(lst[i])

Solution (Python):
from collections import Counter
from itertools import combinations_with_replacement
N = int(input())
L = [i for i in range(1, 100)]
C = Counter()
for i in range(1, N+1):
    C[i] = 0

for c in combinations_with_replacement(L, 3):
    x = c[0]
    y = c[1]
    z = c[2]
    tmp = x**2+y**2+z**2+x*y+y*z+z*x
    if tmp <= N:
        if len(set(c)) == 2:
            C[tmp] += 3
        elif len(set(c)) == 3:
            C[tmp] += 6
        else:
            C[tmp] += 1

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

Solution (Python):
a = [0] * 100000

for i in range(1, 101):
    for j in range(i, 101):
        for k in range(j, 101):
            tmp = 0
            if i != j and j != k:
                tmp = 6
            elif i == j and j != k:
                tmp = 3
            elif i != j and j == k:
                tmp = 3
            elif i == k:
                tmp = 1
            ind = pow(i, 2) + pow(j, 2) + pow(k, 2) + i*j + j*k + k*i
            a[ind] += tmp
N = int(input())
for i in range(1, N+1):
    print(a[i])

Solution (Python):
n = int(input())
l = []
ls = [0]*(n+1)

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

for i in range(1,int(n**0.5)):
    for j in range(1,int(n**0.5)):
        for k in range(1,int(n**0.5)):
            a = cul(i,j,k)
            if a <= n:
                ls[a] += 1
for i in ls[1::]:
    print(i)

Solution (Python):
import math
N = int(input())
S = [0]*N
lim = math.sqrt(N)
lim = math.floor(lim)
for i in range(1,lim):
  for j in range(1,lim):
    for k in range(1,lim):
        temp = int(i**2+ j**2 + k**2 + i*j + j*k + k*i)
        if temp <N+1:
          S[temp-1] += 1
for i in range(N):
  print(S[i])

Solution (Python):
n = int(input())
a = 10 ** 4
l = [0] * (a + 1)


for x in range(1,100):
    for y in range(1,100):
        for z in range(1, 100):
            if x ** 2 + y ** 2 + z ** 2 + x * y + y * z + z * x > a:
                break
            else:
                l[x ** 2 + y ** 2 + z ** 2 + x * y + y * z + z * x] += 1

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

Solution (Python):
import sys
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
read = sys.stdin.buffer.read
sys.setrecursionlimit(10 ** 7)
INF = float('inf')

N = int(input())

answers = [0] * (N + 1)
n = N
for x in range(1, n+1):
    x2 = x ** 2
    for y in range(1, n-x2+1):
        y2 = y ** 2
        xy = x * y
        
        
        for z in range(1, n-x2-y2-xy+1):
            v = x2 + y2 + z ** 2 \
                    + xy + y*z + z*x
            if v > n:
                break
            answers[v] += 1
            
for ans in answers[1:]:
    print(ans)

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

ans = [0] * (10 ** 4 + 1)
for x in range(1, 101):
    for y in range(1, 101):
        for z in range(1, 101):
            s = x * x + y * y + z * z + x * y + y * z + z * x
            if s <= 10 ** 4:
                ans[s] += 1

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