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.



Sample input:
20


Sample output:
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

Submission status: Wrong Answer

Solution code:
N = int(input())

n = N ** (1/2)
n = int(n)


for nn in range(N):
    a = 0
    for x in range(1, n + 1):
        for y in range(1, n + 1):
            for z in range(1, n + 1):
                if x**2 + y**2 + z**2 + x*y + y*z + z*x == nn:
                    a += 1
    print(a)

Submission status: Wrong Answer

Solution code:
import math

N=int(input())
sqN = int(math.sqrt(N))+1

sq=list()
for i in range(1,N):
    sq.append(i*i)

def isSquare(n):
    if n in sq:
        return True
    else:
        return False

ans=list()
for i in range(min(N,6)):
    ans.append(0)

if N>5:
    for m in range(6,N+1):
        cnt = 0
        for x in range(1,sqN):
            for y in range(1,sqN):
                b = x+y
                D = -3*(x*x+y*y)-2*x*y+4*m

                # print(m,x,y,D,isSquare(D))
                if D > 0 and isSquare(D):
                    sqD=sq.index(D)+1
                    if (sqD-b) > 0 and (sqD-b) % 2 == 0:
                        # z= (sqD-b)//2
                        # print(x,y,z)
                        # print(x*x+y*y+z*z+x*y+y*z-m)
                        cnt+=1
                if D < 0:
                    break
        ans.append(cnt)

for a in ans:
    print(a)

Submission status: Wrong Answer

Solution code:
N = int(input())
A  = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 1, 6, 0, 3, 0, 0, 0, 0, 0, 3, 3, 6, 0, 0, 3, 0, 0, 0, 0, 3, 3, 6, 0, 6, 0, 0, 0, 3, 0, 0, 1, 6, 0, 6, 6, 0, 0, 6, 0, 0, 0, 0, 3, 3, 3, 6, 0, 6, 3, 6, 0, 0, 0, 6, 0, 0, 0, 3, 3, 9, 0, 6, 3, 6, 0, 3, 6, 0, 0, 0, 0, 6, 1, 6, 0, 6, 6, 0, 3, 12, 0, 6, 0, 0, 3, 6, 0, 0, 0, 3, 3, 12, 0, 6, 3, 6, 0, 3, 6, 9, 0, 6, 0, 0, 0, 3, 6, 3, 3, 6, 0, 6, 3, 12, 0, 3, 6, 6, 0, 6, 0, 6, 3, 6, 0, 0, 1, 6, 3, 12, 6, 0, 0, 12, 0, 6, 0, 6, 6, 12, 0, 0, 6, 0, 0, 6, 0, 12, 3, 6, 0, 6, 3, 9, 6, 3, 6, 6, 0, 6, 0, 6, 0, 15, 6, 0, 0, 6, 0, 3, 3, 12, 0, 12, 6, 6, 0, 3, 6, 6, 3, 12, 0, 6, 0, 9, 6, 0, 0, 6, 3, 12, 1, 6, 6, 6, 6, 0, 0, 18, 0, 12, 0, 3, 6, 12, 0, 0, 6, 3, 6, 12, 0, 12, 0, 0, 0, 9, 3, 9, 6, 12, 3, 12, 0, 3, 6, 6, 0, 12, 0, 12, 0, 9, 9, 0, 0, 6, 3, 6, 3, 12, 6, 9, 3, 6, 0, 12, 3, 6, 3, 9, 6, 12, 6, 6, 0, 6, 0, 9, 6, 6, 0, 12, 3, 6, 0, 9, 6, 6, 1, 6, 0, 21, 12, 6, 0, 12, 0, 12, 0, 0, 6, 15, 6, 0, 6, 12, 0, 12, 0, 12, 0, 0, 0, 12, 0, 12, 12, 3, 3, 18, 3, 6, 3, 6, 6, 9, 9, 18, 0, 6, 0, 12, 0, 9, 6, 0, 3, 12, 3, 6, 6, 12, 6, 6, 0, 0, 0, 15, 3, 18, 3, 18, 3, 12, 6, 3, 6, 9, 0, 12, 0, 12, 0, 18, 12, 0, 0, 12, 3, 6, 0, 6, 6, 9, 6, 0, 0, 18, 1, 18, 3, 12, 6, 6, 6, 12, 0, 15, 6, 12, 6, 18, 0, 0, 6]
for a in A[:N]:
    print(a)

Submission status: Wrong Answer

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

sqn = int(math.sqrt(n))
count = 0
aset = [0]*(n+1)
for x in range(1,sqn):
    for y in range(x,sqn):
        a = x**2+3*y**2+2*x*y
        for z in range(y,sqn):
            if y!=z:
                a += 2*(z-1)+1+x+y
            if a <= n:
                if x == y and y ==z:
                    aset[a] +=1
                else:
                    aset[a] +=3

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

Submission status: Wrong Answer

Solution code:
ans = 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,42,0,33,0,12,15,15,24,33,9,9,12,39,6,27,21,18,0,45,3,24,18,21,12,24,9,27,9,27,12,24,9,30,0,12,0,24,12,42,12,18,6,45,6,21,12,15,24,27,0,33,6,12,6,30,3,24,18,24,0,30,3,27,27,6,0,15,0,36,12,21,9,36,9,24,12,18,18,48,3,15,0,27,6,45,15,21,15,18,7,21,3,48,24,9,9,36,0,27,6,15,18,39,15,18,12,21,9,39,6,18,15,36,0,24,3,21,18,30,18,33,3,27,0,15,18,33,6,45,0,12,3,48,12,15,12,9,18,54,6,21,24,12,9,15,0,27,9,24,6,39,9,45,12,18,6,36,6,27,12,12,0,57,0,18,15,21,18,24,6,27,6,9,21,24,15,24,0,24,3,45,6,30,21,18,6,24,0,21,21,21,9,39,0,15,3,12,21,39,6,42,15,9,9,33,9,27,15,24,0,36,3,18,27,12,15,24,12,48,3,12,3,48,6,24,0,9,3,36,9,18,9,12,9,12,3,30,18,27,21,48,0,18,9,15,15,30,15,21,6,18,0,60,18,30,18,12,0,48,3,36,18,30,15,27,3,27,12,18,6,33,18,30,0,15,12,12,9,33,15,21,15,39,6,21,15,12,12,69,0,21,0,27,12,30,6,15,12,21,9,27,3,30,18,12,0,36,3,45,12,21,3,33,9,18,0,21,24,27,9,33,0,30,3,30,6,33,30,21,6,36,6,33,21,15,12,30,0,21,9,12,18,24,15,18,9,15,6,39,6,27,9,15,0,30,0,9,30,27,9,39,3,51,6,15,12,24,15,18,0,15,9,63,3,15,18,15,9,33,0,30,15,24,18,24,0,12,3,21,18,48,6,45,18,18,3,21,3,48,15,18,0,30,6,24,21,15,15,36,9,18,6,21,18,36,12,24,0,18,6,33,9,36,21,18,15,27,9,30,15,21,6,30,0,42,12,18,15,36,6,24,12,30,0,30,15,15,15,45,0,39,0,24,30,6,15,24,9,21,3,24,12,45,9,21,0,6,9,42,12,36,9,24,12,33,3,27,21,15,12,24,0,18,9,15,6,21,6,54,9,18,6,48,12,12,15,12,0,48,6,27,12,39,15,27,9,18,0,21,9,42,9,21,0,12,3,27,9,33,21,12,9,42,9,24,21,15,15,39,0,30,0,18,24,18,3,15,18,3,7,39,6,30,24,24,0,45,0,39,6,21,15,24,9,36,6,18,21,57,6,27,0,27,9,27,21,21,24,24,6,36,0,21,9,24,15,33,0,39,3,18,9,39,15,15,15,15,12,51,6,27,9,15,0,18,3,48,24,6,12,54,3,39,9,12,18,18,9,15,0,15,0,54,12,30,21,9,9,45,3,15,24,36,21,24,0,12,9,12,9,42,12,57,3,15,0,24,3,30,21,12,0,51,6,21,21,15,15,39,6,21,12,27,12,21,6,24,0,30,6,33,3,21,12,15,12,21,0,42,12,27,6,33,0,15,3,12,30,51,9,30,12,21,9,27,3,27,30,18,0,27,3,21,21,21,15,33,12,36,0,27,12,51,6,27,0,12,0,54,6,24,12,21,21,30,0,6,24,9,9,27,0,42,9,21,6,42,15,33,12,24,12,39,24,21,21,24,0,30,0,42,15,24,18,27,3,27,15,18,15,45,3,27,0,12,3,36,15,39,6,12,9,33,0,30,18,12,21,57,0,30,3,15,18,27,15,15,18,30,3,27,6,27,18,18,0,21,6,24,21,12,18,48,9,12,6,18,9,51,9,33,0,18,0,27,12,15,15,18,9,42,3,54,24,24,9,30,0,36,6,18,21,30,6,12,12,15,0,27,9,30,9,21,0,33,3,12,12,27,12,39,6,21,15,15,15,27,15,39,0,24,6,60,15,27,21,12,9,27,3,27,12,27,18,33,0,39,6,30,12,24,9,27,18,12,15,42,9,24,18,15,0,63,6,18,15,15,15,33,9,27,0,18,21,24,3,21,0,27,3,30,6,48,27,24,3,30,3,33,9,21,21,39,0,12,12,18,15,54,12,33,15,24,0,24,15,30,15,27,0,21,3,39,24,12,6,33,6,48,3,15,6,45,12,18,0,15,12,36,6,30,15,24,15,27,0,24,27,12,12,36,0,30,0,24,12,36,12,21,9,18,9,36,12,21,21,9,0,39,6,24,18,21,21,18,6,18,12,39,9,24,6,51,0,9,6,27,12,24,15,21,7,54,6,24,12,21,15,51,0,30,3,21,15,27,6,27,12,12,0,57,12,33,24,15,0,24,3,39,18,9,6,36,6,24,9,18,27,60,6,21,0,33,6,24,3,30,18,21,15,51,3,24,27,18,15,24,0,36,0,15,15,39,12,42,15,15,0,36,9,15,24,27,0,30,6,21,24,21,6,48,3,33,0,6,18,39,18,21,0,18,0,39,15,24,12,9,15,45,9,51,9,15,12,27,0,12,12,24,18,42,9,24,21,18,3,33,6,54,6,21,0,24,6,15,30,12,21,42,3,18,9,21,9,27,9,30,0,30,9,36,6,51,21,6,6,30,0,33,21,9,9,39,0,21,3,18,18,33,6,21,9,15,12,39,3,15,24,21,0,51,6,39,24,24,15,42,12,33,6,12,15,45,12,21,0,12,3,45,12,42,18,33,15,18,3,18,24,27,9,36,0,33,9,27,15,12,9,24,9,15,0,51,6,27,18,12,0,51,3,21,9,21,30,27,12,33,12,33,15,51,3,33,0,24,6,12,15,24,18,27,3,39,6,27,12,21,18,48,0,33,3,15,15,33,15,9,15,24,6,45,12,30,18,3,0,21,6,39,18,18,12,57,3,30,0,9,3,36,9,42,0,18,3,24,3,21,12,21,15,27,6,39,24,18,21,30,0,24,0,18,12,72,12,15,15,21,12,39,9,24,9,12,0,39,0,42,30,30,6,24,6,18,15,18,21,21,21,42,0,12,6,45,15,18,21,12,15,45,0,18,12,30,18,42,0,21,0,15,12,45,6,36,12,21,6,33,15,36,12,30,0,48,6,18,21,21,9,33,6,42,6,33,21,21,12,21,0,9,6,39,9,39,24,27,6,27,3,42,15,15,9,27,0,21,12,21,15,48,9,21,12,24,0,27,9,21,18,33,0,42,0,42,24,15,21,27,6,27,9,21,15,48,9,21,0,9,3,63,9,24,12,24,24,21,3,12,27,24,6,30,0,45,6,15,18,24,9,36,12,39,6,15,6,30,15,9,0,39,3,30,18,18,9,30,6,15,0,30,9,45,15,27,0,18,1,39,15,48,15,9,9,51,6,15,15,12,33,45,0,21,6,27,21,21,6,36,15,24,6,54,9,27,24,9,0,42,3,36,12,24,15,57,3,39,12,15,15,21,9,30,0,9,9,33,6,27,33,24,9,27,0,33,30,18,9,24,0,33,3,18,18,48,6,18,15,15,12,48,12,39,15,33,0,30,12,24,15,12,15,36,3,30,6,15,6,48,9,36,0,15,0,42,15,18,24,18,18,45,3,27,12,30,15,18,0,27,9,18,15,39,9,36,18,6,0,27,15,24,12,21,0,45,3,39,15,15,15,69,3,15,9,18,12,39,12,6,0,27,6,21,9,48,18,15,9,33,3,24,18,18,24,57,0,12,3,18,12,54,9,24,12,18,9,30,12,33,21,27,0,39,3,42,18,9,12,21,12,60,0,12,12,33,6,27,0,24,9,33,12,21,18,24,9,36,3,30,24,18,6,51,0,27,12,21,27,30,6,45,9,18,3,57,12,27,24,21,0,45,0,24,21,27,24,27,12,9,9,27,9,36,0,27,0,9,6,27,18,33,9,21,12,60,0,33,21,15,18,24,0,27,3,21,15,42,9,36,18,27,6,36,6,27,27,12,0,27,9,39,12,30,6,39,3,15,6,21,27,36,3,27,0,36,3,39,6,27,21,15,12,24,3,30,24,12,15,45,0,45,9,21,12,21,21,12,15,21,0,42,3,33,15,15,0,15,0,15,24,21,18,45,12,42,12,27,18,36,12,27,0,21,9,45,18,27,9,21,6,63,6,42,18,33,9,27,0,18,0,33,6,24,9,27,15,9,9,30,9,54,27,21,0,51,0,15,18,15,18,54,9,27,0,12,18,33,12,33,0,15,0,27,9,39,27,18,9,24,12,21,18,27,9,54,0,42,9]
n = int(input())
for i in range(n):
  print(ans[i])

Submission status: Wrong Answer

Solution code:
N=int(input())
count=[0]*(10**4+1)
for x in range(1,10**2):
    for y in range(1,10**2):
        for z in range(1,10**2):
            n=x**2+y**2+z**2+x*y+y*z+z*x
            if n<=10**4:
                count[n]+=1
for i in range(1,N):
    print(count[i])

Submission status: Wrong Answer

Solution code:
n = int(input())

n_list = [0]*50000
for x in range(1,51):
    for y in range(1,51):
        for z in range(1,51):
            index = x*x + y*y + z*z + x*y + y*z + z*x
            n_list[index] = n_list[index]+1

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

Submission status: Wrong Answer

Solution code:
n = int(input())

from collections import defaultdict
d = defaultdict(int)

for i in range(1,100):
  for j in range(1,100):
    for k in range(1,100):
      d[i**2+j**2+k**2+i*j+j*k+k*i]+=1

for j in range(1,n):
  if d[j]:
    print(d[j])
  else:
    print(0)

Submission status: Wrong Answer

Solution code:
import math
import collections
import fractions
import itertools
import functools
import operator

def solve():
    n = int(input())
    for i in range(1,n+1):
        cnt = 0
        for x in range(1,int(math.sqrt(i))-4):
            for y in range(1,int(math.sqrt((i-x)))+1):
                rema = i - x**2 - y**2 - x*y
                if rema > 0:
                    for z in range(1, rema):
                        if z**2 + (x+y)*z == rema:
                            cnt += 1
                            break
                else:
                    break
        print(cnt)
    return 0

if __name__ == "__main__":
    solve()

Submission status: Wrong Answer

Solution code:
import itertools

N=int(input())
L=[0]*(10**4+10)
X=[x for x in range(1,11)]
plus=[0,1,3,6]

for v in itertools.combinations_with_replacement(X,3):
  x,y,z=v[0],v[1],v[2]
  temp=len(set(v))
  L[x**2+y**2+z**2+x*y+y*z+z*x]+=plus[temp]


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

Submission status: Wrong Answer

Solution code:
a, b = 1, 1
N = int(input())
test = (a ** 2) * 3 + b ** 2 + a * b * 2
hoge = 2
print(a,b,test)
for i in range(1, N + 1):
    x = 0
    while True:

        if test <= i:
            if test == i:
                if a == b:
                    x += 1
                else:
                    x += 3
            if b - 1 <= 0:
                hoge += 1
                b = hoge - 1
                a = 1
            else:
                b -= 1
                a += 1
            test = (a ** 2) * 3 + b ** 2 + a * b * 2

        else:
            print(x)
            break