If someone can put this into stuff people can understand, that'd be great, but I'm not very good with code. So I'm just going to describe it. n = size of one dimension in square grid x = number of possible combinations in bounding box y = number of bounding boxes To find number of combinations in any given grid, start with the highest size bounding box possible, in which possibilities will equal $$ y \times n^2 $$ For the next bounding box size, increase y by 1 and decrease n by 1. So like this: $$ y+1 \times (n - 1)^2 $$ Keep adding and subtracting from one side until n = 1. Then, add all the products up.