Dhoni has 3 types of water bottles. He has exactly aaa bottles of volume 0.5 liters, bbb bottles of volume 1 liter, and ccc bottles of volume 2 liters. Your task is to help Dhoni count the number of ways to carry exactly nnn liters of water. Two variants are different from each other only if they differ in the number of bottles of at least one kind.

This is a companion discussion topic for the original entry at https://toph.co/p/water