I have been working with this code on a project with the same LED Strip. I have it working with 12 segments and will post the code that I have working when I get home.
Note: these LED strings are on clearance, they have been replaced with a similar set, I have not worked with them and will not. The adafruit neopixels look much easier to work with and I will go with them for future LED projects.
I will comment up my code with what I understand of its function, including PROGMEM.