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 in Rust (1.42.0) (judge verdict: Accepted)

use input::Input;

fn main() {
    let mut input = Input::default();

    let n = input.parse::<u32>();

    for i in 0..n {
        println!("{}", f(i + 1));
    }
}

fn f(n: u32) -> u32 {
    let mut res = 0u32;
    for i in 1..=n {
        if i * i > n {
            break;
        }
        for j in i..=n {
            if j * j > n {
                break;
            }
            for k in j..=n {
                if k * k > n {
                    break;
                }
                if i * i + j * j + k * k + i * j + j * k + k * i == n {
                    if i == j && j == k {
                        res += 1;
                    } else if i != j && j != k && k != i {
                        res += 6;
                    } else {
                        res += 3;
                    }
                }
            }
        }
    }
    res
}

#[allow(dead_code)]
pub mod input {
    #[derive(Default)]
    pub struct Input(Vec<String>);

    impl Input {
        pub fn read_line(&mut self) -> String {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).ok().expect("read error");
            s
        }
        pub fn parse<T: std::str::FromStr>(&mut self) -> T {
            let x = if let Some(x) = self.0.pop() {
                x
            } else {
                let s = self.read_line();
                self.0 = s.split_whitespace().map(String::from).rev().collect();
                self.0.pop().expect("reached EOF")
            };
            x.parse().ok().expect("parse error")
        }
    }
}