Generalized taxicab number

Alright kiddo, have you ever played a game where you have a big grid with squares on it, and you have to move around on the grid by only taking certain sized steps? Let's say you can only take steps that are 1 square long, or 2 squares long.

Now imagine you're trying to get to a certain point on the grid, but you don't care about the path you take - you just want to get there in the least amount of steps possible. This is where a generalized taxicab number comes in.

A generalized taxicab number is a way of measuring how many steps you need to take, using any combination of step sizes, to get from one point on the grid to another. So, for example, let's say you want to get from point A to point B. If you can take steps that are 1 square long or 2 squares long, you might end up taking a path that looks like this:

1 square, 1 square, 2 squares, 2 squares, 2 squares, 2 squares, 1 square

That's a total of 11 steps. A generalized taxicab number would tell you that the distance between point A and point B is 11.

Does that make sense? Basically, it's a way of measuring distance when you can only take certain sized steps.