Attempting to make a round LED Matrix

Questions
1

I am attempting to build a round LED matrix. Total size will end up being 137 pixels. I would like to use the 2d matrix because some of those effects are really awesome. How would I go about mapping this so that it would work like a 13x13 square matrix skipping the missing LEDs.

Number of LEDs per row, centered:
5
9
11
11
13
13
13
13
13
11
11
9
5

2

So basically you are building a ring . Look here for an example of the mapping for that as a matrix Noobie 241 led ring - #3 by ALDIY