p02608 AIsing Programming Contest 2020 - XYZ Triplets
Problem Description
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).
Example
Input
20
Output
0 0 0 0 0 1 0 0 0 0 3 0 0 0 0 0 3 3 0 0
Contest Information
- Contest ID: 0
- Problem Index:
- Points: 0.0
- Rating: 0
- Tags:
- Time Limit: {'seconds': 2, 'nanos': 0} seconds
- Memory Limit: 1073741824 bytes
Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.