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):
import sys
sys.setrecursionlimit(10000000)
MOD = 10 ** 9 + 7
INF = 10 ** 15
ans = [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, 24, 15, 18, 0, 24, 12, 45, 12, 6, 0, 54, 0, 15, 21, 6, 6, 30, 6, 18, 12, 24, 18, 30, 6, 36, 0, 12, 3, 24, 12, 18, 18, 18, 12, 24, 0, 33, 12, 27, 6, 42, 0, 18, 6, 9, 15, 30, 6, 30, 6, 12, 6, 18, 6, 33, 15, 30, 0, 36, 3, 27, 21, 33, 24, 30, 9, 24, 0, 12, 18, 33, 6, 6, 0, 18, 3, 57, 12, 24, 18, 30, 9, 18, 0, 18, 12, 27, 12, 36, 0, 36, 6, 12, 6, 27, 12, 30, 9, 24, 6, 39, 18, 12, 24, 12, 0, 30, 0, 30, 6, 15, 15, 18, 3, 24, 18, 9, 12, 30, 9, 30, 0, 18, 6, 42, 18, 30, 0, 6, 10, 48, 0, 24, 12, 12, 18, 48, 0, 30, 3, 30, 15, 18, 6, 24, 18, 18, 0, 42, 6, 36, 15, 24, 0, 42, 12, 21, 24, 12, 12, 24, 0, 12, 6, 18, 18, 60, 6, 30, 0, 12, 0, 24, 0, 12, 18, 30, 15, 42, 0, 33, 30, 6, 6, 12, 0, 42, 3, 27, 6, 33, 12, 36, 12, 18, 0, 30, 6, 18, 12, 12, 0, 18, 6, 15, 27, 27, 6, 42, 6, 36, 9, 18, 30, 33, 9, 30, 0, 6, 6, 54, 6, 36, 24, 24, 0, 30, 3, 12, 6, 21, 24, 30, 0, 24, 0, 24, 12, 42, 9, 42, 21, 12, 12, 27, 12, 27, 6, 12, 0, 48, 6, 12, 18, 12, 12, 36, 6, 30, 0, 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30, 6, 27, 27, 24, 0, 54, 6, 21, 18, 21, 6, 36, 15, 36, 3, 30, 12, 6, 18, 30, 0, 18, 6, 54, 0, 30, 21, 36, 9, 30, 6, 30, 24, 24, 6, 30, 0, 36, 12, 9, 24, 24, 12, 18, 9, 30, 0, 48, 12, 24, 12, 12, 0, 48, 0, 18, 12, 24, 24, 30, 6, 18, 12, 21, 12, 24, 0, 66, 0, 12, 0, 30, 9, 24, 24, 18, 13, 42, 3, 18, 18, 27, 24, 24, 0, 30, 6, 15, 18, 39, 12, 12, 9, 36, 12, 54, 12, 42, 18, 6, 0, 36, 0, 51, 18, 12, 0, 66, 12, 24, 0, 6, 24, 51, 12, 24, 0, 24, 0, 33, 6, 18, 18, 30, 6, 42, 3, 18, 30, 15, 15, 30, 0, 30, 6, 30, 12, 48, 12, 24, 12, 12, 9, 36, 6, 36, 6, 12, 0, 30, 0, 24, 21, 24, 15, 42, 12, 24, 6, 9, 18, 15, 9, 42, 0, 24, 12, 66, 12, 30, 24, 6, 9, 54, 0, 36, 12, 21, 12, 36, 0, 24, 3, 24, 15, 36, 6, 30, 24, 12, 6, 33, 6, 39, 21, 30, 0, 42, 6, 12, 30, 30, 18, 36, 0, 48, 3, 36, 12, 30, 18, 18, 0, 24, 0, 30, 6, 33, 21, 24, 6, 18, 12, 24, 12, 12, 15, 48, 0, 24, 6, 21, 21, 60, 6, 24, 12, 18, 0, 30, 12, 15, 12, 24, 0, 24, 3, 60, 27, 18, 12, 30, 3, 24, 9, 21, 12, 60, 18, 24, 0, 24, 9, 33, 6, 36, 12, 24, 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30, 42, 12, 36, 0, 117, 36, 54, 36, 24, 0, 96, 3, 72, 36, 57, 27, 54, 6, 54, 21, 36, 12, 66, 33, 60, 0, 30, 24, 24, 15, 63, 30, 42, 24, 78, 9, 39, 30, 24, 24, 138, 0, 42, 0, 54, 24, 57, 12, 30, 24, 42, 18, 54, 6, 60, 33, 24, 0, 72, 6, 84, 24, 42, 6, 66, 15, 36, 0, 42, 48, 51, 18, 66, 0, 60, 3, 60, 12, 60, 57, 42, 9, 72, 12, 60, 42, 27, 24, 60, 0, 42, 18, 24, 30, 48, 30, 36, 18, 30, 9, 78, 12, 51, 18, 30, 0, 60, 0, 12, 57, 51, 18, 78, 6, 102, 12, 30, 24, 48, 27, 36, 0, 30, 12, 126, 6, 27, 36, 30, 18, 66, 0, 60, 30, 48, 36, 48, 0, 24, 6, 39, 24, 96, 12, 90, 33, 36, 6, 39, 6, 90, 27, 36, 0, 60, 12, 45, 42, 30, 30, 72, 12, 36, 9, 39, 36, 69, 24, 48, 0, 36, 6, 66, 15, 72, 39, 36, 27, 54, 18, 57, 30, 42, 12, 60, 0, 84, 24, 36, 27, 72, 12, 48, 21, 60, 0, 51, 30, 27, 30, 90, 0, 78, 0, 42, 57, 12, 30, 48, 18, 42, 6, 48, 24, 90, 15, 42, 0, 12, 15, 84, 24, 72, 18, 48, 21, 66, 3, 54, 42, 30, 24, 48, 0, 36, 18, 27, 12, 42, 9, 108, 18, 36, 12, 96, 24, 21, 30, 24, 0, 96, 9, 54, 18, 75, 30, 54, 18, 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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]
def main():
    N = int(input())
    for i in range(N):
        print(ans[i])
if __name__ == '__main__':
    main()