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())
A=[0,0,0,0,0,1,0,0,0,0,3,0,0,0,0,0,3,3,0,0,0,0,0,1,6,0,3,0,0,0,0,0,3,3,6,0,0,3,0,0,0,0,3,3,6,0,6,0,0,0,3,0,0,1,6,0,6,6,0,0,6,0,0,0,0,3,3,3,6,0,6,3,6,0,0,0,6,0,0,0,3,3,9,0,6,3,6,0,3,6,0,0,0,0,6,1,6,0,6,6,0,3,12,0,6,0,0,3,6,0,0,0,3,3,12,0,6,3,6,0,3,6,9,0,6,0,0,0,3,6,3,3,6,0,6,3,12,0,3,6,6,0,6,0,6,3,6,0,0,1,6,3,12,6,0,0,12,0,6,0,6,6,12,0,0,6,0,0,6,0,12,3,6,0,6,3,9,6,3,6,6,0,6,0,6,0,15,6,0,0,6,0,3,3,12,0,12,6,6,0,3,6,6,3,12,0,6,0,9,6,0,0,6,3,12,1,6,6,6,6,0,0,18,0,12,0,3,6,12,0,0,6,3,6,12,0,12,0,0,0,9,3,9,6,12,3,12,0,3,6,6,0,12,0,12,0,9,9,0,0,6,3,6,3,12,6,9,3,6,0,12,3,6,3,9,6,12,6,6,0,6,0,9,6,6,0,12,3,6,0,9,6,6,1,6,0,21,12,6,0,12,0,12,0,0,6,15,6,0,6,12,0,12,0,12,0,0,0,12,0,12,12,3,3,18,3,6,3,6,6,9,9,18,0,6,0,12,0,9,6,0,3,12,3,6,6,12,6,6,0,0,0,15,3,18,3,18,3,12,6,3,6,9,0,12,0,12,0,18,12,0,0,12,3,6,0,6,6,9,6,0,0,18,1,18,3,12,6,6,6,12,0,15,6,12,6,18,0,0,6,0,9,12,0,18,0,6,3,12,0,12,12,0,0,12,0,3,6,12,6,18,9,18,0,9,6,18,0,6,0,6,3,27,6,6,6,6,3,6,0,12,6,9,0,6,0,18,0,9,9,15,3,12,6,6,3,9,6,12,12,18,0,18,0,6,6,21,6,0,0,6,3,15,6,12,6,18,0,0,0,12,6,6,3,6,4,18,6,12,6,3,9,30,0,18,0,6,6,12,6,6,9,12,0,18,6,18,0,6,0,12,0,6,12,6,3,18,0,6,6,6,6,15,3,24,0,6,3,18,0,12,6,12,6,24,0,15,18,9,6,0,0,18,3,6,0,15,12,12,6,6,0,18,0,6,3,12,0,12,6,6,9,9,6,24,3,24,0,9,12,6,6,12,0,12,0,21,9,15,6,12,3,18,3,12,6,12,6,0,0,12,0,12,6,24,0,6,12,6,1,9,6,12,6,24,0,18,3,12,6,6,12,24,0,12,6,15,6,18,0,18,0,0,0,18,9,21,12,0,6,18,0,9,6,6,6,12,0,12,0,9,9,27,6,6,3,18,6,21,6,6,12,12,0,12,0,24,12,0,0,24,3,24,6,12,12,18,0,0,0,12,0,18,3,15,6,12,9,6,0,15,6,9,12,24,0,12,3,6,6,21,6,18,3,18,0,21,12,15,6,6,0,12,3,12,9,18,9,12,6,6,6,24,0,18,3,24,0,6,6,0,6,9,6,6,4,30,0,18,12,9,6,24,0,18,0,9,12,21,6,6,12,12,0,18,0,21,15,12,0,12,6,12,12,18,0,18,0,6,0,9,12,18,6,30,0,0,0,24,6,9,3,12,6,30,3,6,12,6,12,12,0,36,0,6,3,27,12,12,6,6,6,24,0,12,6,12,0,18,0,18,15,18,3,18,6,12,6,6,12,3,6,6,0,12,3,39,3,12,12,12,3,18,0,21,12,21,6,18,0,12,0,9,9,12,9,24,9,12,6,12,6,33,0,6,0,18,0,9,15,12,6,24,6,6,3,15,6,15,12,18,0,18,1,18,6,12,6,6,0,24,6,24,12,18,6,24,0,6,6,12,15,24,0,24,6,6,0,18,0,15,18,12,0,24,0,12,6,12,12,18,6,24,0,0,6,24,3,12,0,12,6,30,9,6,12,24,12,12,0,15,18,12,0,18,0,24,6,15,6,18,3,18,3,12,6,24,12,12,12,6,0,36,0,18,3,6,12,6,9,12,0,3,12,36,0,30,0,12,0,18,6,12,9,12,6,24,3,18,12,15,9,24,0,18,6,18,9,18,12,6,6,24,3,24,0,12,12,12,0,6,0,27,12,18,3,30,3,18,6,0,12,15,6,18,0,24,0,9,6,9,12,18,7,24,0,24,12,15,12,24,0,24,0,6,9,30,9,6,6,0,9,33,12,36,0,12,0,18,0,6,21,12,6,36,6,0,3,18,6,12,6,24,0,12,3,24,6,9,12,6,6,30,6,18,12,9,9,12,0,30,3,18,3,27,6,30,12,12,0,24,0,27,12,6,0,24,3,18,18,9,6,18,0,12,3,33,18,12,9,6,0,12,6,30,0,24,12,12,0,30,6,6,6,0,6,24,0,12,0,18,15,33,6,30,15,18,0,9,12,24,9,12,0,18,6,27,18,15,6,18,3,24,0,6,6,36,12,18,0,12,3,30,3,12,6,12,15,6,0,18,12,15,9,30,0,18,6,12,12,18,6,6,3,24,1,27,12,18,6,18,0,24,0,18,15,15,21,30,6,12,12,18,0,30,6,24,0,6,0,18,6,36,12,6,6,36,0,6,12,12,12,24,0,30,0,9,6,18,0,18,12,12,6,24,6,9,15,12,0,12,6,30,9,18,0,42,3,18,6,12,18,33,12,12,0,18,0,21,12,12,12,24,6,30,0,27,18,6,12,6,0,24,0,18,15,30,0,18,12,6,0,21,6,21,12,24,0,30,0,6,6,6,12,24,0,30,12,9,12,21,3,24,0,12,3,21,18,9,18,18,6,30,3,42,6,21,6,30,0,6,3,24,9,36,6,6,9,12,6,18,12,33,9,12,0,24,9,9,6,3,18,36,6,18,0,24,6,6,6,18,0,12,0,30,3,39,12,12,7,18,0,15,18,18,9,36,0,24,6,6,18,30,0,18,9,18,3,24,6,21,12,24,0,30,3,33,24,12,6,18,6,6,6,18,6,18,12,18,0,24,6,36,3,18,6,0,12,30,0,9,24,18,0,24,0,18,0,0,12,30,15,30,6,18,3,30,0,24,18,12,0,36,3,24,12,15,18,18,6,24,3,24,12,18,12,24,0,0,6,39,6,24,3,18,3,42,6,12,12,15,9,30,0,12,0,18,6,18,12,24,15,12,0,12,12,30,12,12,0,18,0,15,15,18,18,30,3,24,12,9,6,48,0,18,0,30,0,21,6,12,12,24,12,18,3,48,24,6,6,18,0,36,0,12,15,27,6,12,12,18,6,27,6,12,9,18,0,24,6,18,18,21,0,36,0,12,0,18,12,21,18,24,0,12,1,18,9,21,18,6,9,42,3,36,12,12,12,30,0,12,6,21,12,36,6,24,9,12,6,12,12,24,12,18,0,42,0,15,6,15,15,42,6,30,6,12,12,18,12,18,0,6,6,36,0,30,18,6,0,6,0,30,18,18,0,42,0,18,6,15,18,24,0,12,6,36,9,33,12,12,12,18,0,36,0,21,21,15,18,18,15,18,0,18,6,42,6,24,0,18,3,42,6,18,12,12,12,18,0,15,12,18,12,36,0,30,12,3,21,18,0,30,6,24,0,27,12,18,12,6,0,12,0,36,15,15,3,36,12,18,6,30,6,33,12,12,0,12,6,24,6,54,18,12,3,36,9,9,12,12,18,36,0,6,0,21,15,27,9,24,12,30,6,24,6,27,18,12,0,30,0,21,12,18,6,30,0,18,0,21,18,21,6,30,0,24,3,6,6,15,27,12,10,42,6,36,12,12,6,24,0,24,6,12,12,48,6,18,12,0,3,51,6,30,6,24,0,24,0,30,21,15,12,24,9,18,6,18,12,30,9,24,0,18,0,27,18,9,6,18,9,54,0,18,24,21,18,12,0,24,0,12,0,30,9,30,12,6,9,24,6,15,15,18,0,30,3,33,18,21,12,42,3,30,6,6,24,27,6,12,0,24,3,42,6,42,9,12,6,18,6,24,12,12,12,54,0,6,12,18,6,18,18,30,12,30,0,18,0,27,18,24,0,18,0,15,24,21,6,24,3,36,6,6,6,45,21,18,0,18,6,33,3,18,0,24,15,30,0,30,24,12,6,36,0,24,3,21,24,18,15,30,3,12,6,42,12,12,12,6,0,54,6,30,15,24,18,24,6,12,0,9,6,30,0,48,0,24,0,15,12,39,12,24,6,24,6,15,30,12,6,24,0,24,3,24,12,24,6,6,18,12,4,54,6,21,18,18,0,36,6,24,9,30,12,24,9,36,6,12,18,42,3,30,0,6,9,21,6,12,30,30,6,30,0,27,12,9,18,30,0,36,0,18,9,42,6,24,12,0,6,51,12,24,12,12,0,18,6,12,18,6,6,36,3,54,9,18,6,27,12,18,0,30,0,39,9,18,18,12,9,30,6,21,12,27,18,24,0,12,0,42,18,42,6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for i in range(N):
  print(A[i])