I was investigating the number of unique grid points in a Cartesian coordinate system if I were to start at a corner (say coordinate 1,1,1), and make one step in each of the three positive directions (coordinates 1,2,1; 2,1,1; and 1,1,2). Now I went from 1 point to 3 points. I repeat the same process for the three new points and I found 6 unique new points, and then from the 6 I found 10. It turns out this 1,3,6,10 sequence (which I predict the next number is 15) is called the triangle numbers. My question is, what is the name of the algorithm that finds the number of unique grid points in the way I did it? I knew there must be an existing pattern/equation out there but I don't know what it is called. Thanks!