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

Solution (Python):


import sys
import math
from decimal import Decimal, ROUND_DOWN
from collections import deque
from itertools import combinations
import copy

debug = False

def log(text):
    if debug:
        print(text)

def parse_input(lines_as_string = None):

    global debug
    lines = []
    if lines_as_string is None:
        debug = False
        for line in sys.stdin:
            lines.append(line.strip())
    else:
        debug = True
        lines = [e for e in lines_as_string.split("\n")][1:-1]

    (n, ) = [int(e) for e in lines[0].split(' ')]


    return (n, )


def solve(n):


    
    

    result = []
    for m in range(1, n+1):
        cnt = 0
        for i in range(1, 101):
            for j in range(i, 101):
                t = i*i + j*j + i*j
                for k in range(j, 101):
                    tmp =  t + k*k + j*k + k*i
                    if tmp == m:
                        if i < j and j < k:
                            cnt = cnt + 6
                        elif i == j and j == k:
                            cnt = cnt + 1
                        else:
                            cnt = cnt + 3
                    elif tmp > m:
                        break
                        
        result.append(cnt)

    return result
    


def main():
    
    result = solve(*parse_input())
    if isinstance(result, list):
        for r in result:
            print("%s" % r, sep='')
    else:
        print("%s" % result, sep='')

if __name__ == '__main__':

    main()

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

highest = int(math.sqrt(n))
l = [0]*n
cal = 0

for x in range(1, highest+1):
  for y in range(1, highest+1):
    for z in range(1, highest+1):
      cal = x**2 + y**2 + z**2 + x*y + y*z + z*x
      if cal > n:
        continue
      else:
        l[cal-1] += 1
        
for i in range(len(l)):
  print(l[i])

Solution (Python):
import math
N = int(input())
sqN = math.floor(math.sqrt(N))
ansdict = {i+1:0 for i in range(N)}

for z in range(1, sqN+1):
  for y in range(1, sqN+1):
    for x in range(1, sqN+1):
      try:
        ansdict[x**2 + y**2 + z**2 + x*y + y*z + z*x] += 1
      except KeyError:
        continue

for num in ansdict.values():
  print(num)

Solution (Python):
from collections import deque

def getInts():
    return [ int(x) for x in input().split() ]

cache = {}
def f(x,y,z):
    if (x,y,z) in cache:
        return cache[(x,y,z)]
    
    v =  x**2+y**2+z**2+x*y+y*z+z*x
    cache[(x,y,z)] = v
    return v

[N] = getInts()
Q = deque([(0,0,0)])
V = set()
l = [f(0,0,0)]
ans = {}
while Q:
    x,y,z = Q.pop()
    l = list(filter(lambda x: x not in V and x[0]>=1 and x[1]>=1 and x[2]>=1 and f(*x) <= N, [ (x+1,y,z),(x,y+1,z),(x,y,z+1),(x+1,y+1,z+1) ]))
    for x in l:
        V.add(x)
        Q.appendleft(x)
        v = f(*x)
        if v not in ans:
            ans[v] = 1
        else:
            ans[v] += 1
for i in range(1, N+1):
    if i not in ans:
        print(0)
    else:
        print(ans[i])

Solution (Python):
n = int(input())
t = []
ans = [0]*(10**4+5)
def calc(x, y, z):
    return x**2+y**2+z**2 + x*y + y*z + z*x

for x in range(1, 10**2):
    for y in range(1, 10**2):
        for z in range(1, 10**2):
            t.append(calc(x,y,z))

for i in t:
    if i < 10**4+5:
        ans[i] += 1
for i in range(1,n+1):
    print(ans[i])