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: Accepted

Solution code:
a = 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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,]
n=int(input())
for i in range(n):
	print(a[i])

Submission status: Accepted

Solution code:
from collections import defaultdict

N = int(input())
X = [_ for _ in range(1,101)]
Y = [_ for _ in range(1,101)]
Z = [_ for _ in range(1,101)]

D = defaultdict(int)
for x in X:
    for y in Y:
        for z in Z:
            n = (x+y)**2 + (y+z)**2 + (z+x)**2
            if n % 2 == 0:
                if x == y == z:
                    D[n//2] += 1
                elif x != y and y != z and z != x:
                    D[n//2] += 1
                else:
                    D[n//2] += 1
for i in range(1,N+1):
    print(D[i])

Submission status: Accepted

Solution code:
n = int(input())

ans = [0]*10001

for a in range(1,101):
    for b in range(1,101):
        for c in range(1,101):
            x = a**2+b**2+c**2+a*b+b*c+a*c
            if x<10001:
                ans[x] += 1
            else:
                break

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

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
import sys
import math
sys.setrecursionlimit(500005)


def solve(N: int):
    rn = math.ceil(math.sqrt(N))
    arr = [0] * N
    counter = 0
    for x in range(1,rn+1):
        for y in range(1,rn+1):
            for z in range(1,rn+1): 
                if ((x*x+y*y+z*z+x*y+y*z+z*x) > N ):
                    continue
                else:
                    arr[(x*x+y*y+z*z+x*y+y*z+z*x) -1 ] += 1
    for i in arr:
        print(i)

# Generated by 1.1.7.1 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    solve(N)

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
from math import sqrt

n = int(input())
for i in range(1, n + 1):
    if i <= 5:
        print(0)
        continue
    cnt = 0
    ub = int(-1 + sqrt(i - 2))
    for y in range(1, ub + 1):
        for z in range(1, ub + 1):
            tmp = 4 * i - 3 * y * y - 3 * z * z - 2 * y * z
            if tmp < 0:
                continue
            s = int(sqrt(tmp))
            if s * s != tmp:
                continue
            if (s - y - z) % 2 != 0:
                continue
            if s > y + z:
                cnt += 1
    print(cnt)

Submission status: Accepted

Solution code:
import sys
import math
import heapq
from collections import defaultdict, deque
from decimal import *
def r():
    return int(input())
def rm():
    return map(int,input().split())
def rl():
    return list(map(int,input().split()))

ans=defaultdict(int)
n=r()
for i in range(1,100):
    for j in range(1,100):
        for k in range(1,100):
            add=(i+j+k)**2-(i*j)-(j*k)-(k*i)
            ans[add]+=1
for i in range(1,n+1):
    print(ans[i])

Submission status: Accepted

Solution code:
import math
n = int(input())
c = [0 for _ in range(n)]
ln = int(math.sqrt(n+1))

for x in range(1, ln+1):
  for y in range(1, ln+1):
    for z in range(1, ln+1):
      s = x*x + y*y + z*z + x*y + y*z + z*x
      if(s-1 < n):
        c[s-1] += 1
      else:
        break
        
for i in c:
  print(i)