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

def readinput():
    n=int(input())
    return n

def main(n):
    f=[0]*n
    for i in range(1,n+1):
        sqrt2n=int(sqrt(2*i))+1
        
        for x in range(1,sqrt2n):
            for y in range(1,sqrt2n-x+1):
                if (x+y)**2>2*i:
                    break
                for z in range(1,sqrt2n-x+1):
                    v=(x+y)**2+(y+z)**2+(z+x)**2
                    if v>2*i:
                        break
                    
                    if v==2*i:
                        f[i-1]+=1
                        
                        
    return f

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

def main2(n):
    sqrt2n=int(sqrt(2*n))+1
    cntbl=[0]*(10**4+1)
    for x in range(1,sqrt2n):
        for y in range(1,sqrt2n):
            for z in range(1,sqrt2n):
                v=F(x,y,z)
                if v>n:
                    break
                cntbl[v]+=1
    return cntbl


if __name__=='__main__':
    n=readinput()
    ans=main2(n)
    for i in range(1,n+1):
        print(ans[i])

Solution (Python):
import math
import sys


def input(): return sys.stdin.readline().strip()
def I(): return int(input())
def LI(): return list(map(int, input().split()))
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def S(): return input()
def LS(): return input().split()


INF = float('inf')


n = I()
cnt = [0] * 10001
r_n = int(math.sqrt(n)) + 1
for x in range(1, r_n):
    for y in range(1, r_n):
        for z in range(1, r_n):
            v = x**2 + y**2 + z**2 + x*y + y*z + z*x
            if v <= n:
                cnt[v] += 1

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

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

ans = [0] * n
for x in range(1, 101):
    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 >= 1 and a <= n:
                ans[a - 1] += 1

for a in ans:
    print(a)

Solution (Python):
import sys
def I(): return int(sys.stdin.readline().rstrip())

def f(x,y,z):
    return x*x+y*y+z*z+x*y+y*z+z*x

def Main():
    n = I()
    c = [0]*n
    fa = True
    for i in range(1,n+1):
        if n<f(i,1,1):  break
        for j in range(1,n+1):
            if n<f(i,j,1):  break
            for k in range(1,n+1):
                tmp = f(i,j,k)
                if n<tmp:   break
                c[tmp-1] += 1

    for rep in c:
        print(rep)
    return

if __name__=='__main__':
    Main()

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

f=[0]*(10001)
for x in range(1,101):
    for y in range(1,101):
        for z in range(1,101):
            tmp=x*x+y*y+z*z+x*y+y*z+z*x
            if tmp>10000:continue
            f[tmp]+=1

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

Solution (Python):
def main():
    n = int(input())
    s = 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66,0,12,36,78,36,42,0,36,0,78,24,48,24,18,30,90,15,96,18,27,21,54,0,24,21,48,27,84,18,48,42,36,6,66,12,108,12,42,0,48,9,27,60,21,36,84,6,36,18,42,18,54,18,60,0,60,15,72,9,99,42,12,12,60,0,57,42,18,18,78,0,42,6,36,36,63,9,42,15,30,18,78,6,24,48,42,0,102,12,75,45,42,30,84,24,66,9,24,30,90,24,42,0,24,3,84,21,84,33,66,24,36,6,36,48,51,18,72,0,66,18,54,30,24,18,48,18,30,0,102,12,45,36,24,0,102,3,42,15,42,54,54,21,66,24,66,30,102,3,66,0,48,12,24,30,45,36,54,6,78,9,48,24,39,36,96,0,66,6,27,27,60,30,18,30,48,12,90,24,60,36,6,0,42,12,78,36,36,24,114,6,60,0,18,6,69,18,84,0,36,6,48,6,39,24,42,24,54,6,72,48,36,42,60,0,48,0,36,18,138,24,30,30,42,18,75,18,48,18,24,0,78,0,78,57,60,9,48,9,36,30,30,42,42,39,84,0,24,12,87,27,30,42,24,24,90,0,36,24,60,36,84,0,42,0,30,21,87,12,72,24,42,12,60,30,72,21,60,0,96,12,30,42,39,18,66,12,84,12,63,42,42,24,42,0,18,6,78,15,75,45,54,12,54,6,84,30,30,18,54,0,42,24,39,27,96,18,42,21,48,0,54,18,33,36,66,0,84,0,75,48,30,42,54,12,54,15,42,30,96,18,42,0,18,6,123,15,48,24,48,39,42,6,21,54,45,12,60,0,90,12,30,36,45,18,72,21,78,12,30,12,60,30,18,0,78,6,60,36,33,18,60,12,30,0,60,18,90,30,54,0,36,1,78,27,84,30,18,15,102,9,27,30,24,57,90,0,42,9,48,42,42,12,72,27,48,9,108,18,48,48,18,0,84,6,66,24,48,21,114,6,78,24,30,30,42,18,60,0,18,12,63,9,51,66,48,15,54,0,66,60,36,18,48,0,66,6,36,30,96,9,36,30,30,24,93,24,72,24,66,0,60,24,48,30,24,30,72,6,60,12,30,12,93,18,72,0,30,0,81,30,36,48,36,30,90,6,54,24,57,24,36,0,54,18,36,24,78,18,72,33,12,0,51,30,48,24,42,0,90,3,78,30,30,27,138,6,30,18,36,24,75,24,12,0,54,12,42,18,84,36,30,18,66,6,45,36,36,48,114,0,24,6,30,21,108,15,48,18,36,18,57,24,63,42,54,0,78,6,81,36,18,24,42,18,120,0,24,24,66,12,54,0,48,12,66,18,42,36,48,18,72,6,48,48,33,6,102,0,54,24,39,54,60,12,90,18,36,3,111,24,51,48,42,0,90,0,45,36,54,48,54,24,18,18,51,18,72,0,54,0,18,12,54,36,57,18,42,18,120,0,63,42,27,36,48,0,54,6,39,30,81,18,72,33,54,9,72,12,54,54,24,0,54,15,75,24,60,12,78,6,30,12,39,54,72,6,54,0,72,6,78,12,54,39,30,15,48,6,57,48,18,24,90,0,90,18,42,24,39,42,24,30,42,0,84,6,66,30,30,0,30,0,27,42,39,33,90,24,84,18,51,36,69,24,54,0,42,18,87,33,51,18,42,9,126,9,84,36,66,18,54,0,36,0,66,12,48,15,54,30,18,18,60,18,96,54,42,0,102,0,27,36,30,36,108,15,54,0,24,36,60,24,66,0,30,0,54,15,75,48,36,18,48,24,36,36,54,15,108,0,84,18]
    return s[:n]
  
print(*main())

Solution (Python):


from pprint import pprint
from collections import deque, defaultdict
import itertools
import math
import sys

sys.setrecursionlimit(10 ** 6)
INF = float('inf')


N = int(input())


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


xyz_dict = defaultdict(int)
num_dict = defaultdict(int)
for x in range(1, 100):
    for y in range(1, 100):
        for z in range(1, 100):
            num = g(x, y, z)
            if (x, y, z) in xyz_dict:
                continue
            xyz_dict[(x, y, z)] = 1
            num_dict[num] += 1


for n in range(1, N+1):
    print(num_dict[n])