Ok so I decided to do some real research into this and it seemed that corals that look like the one pictured above are either referred to as Dendrophyllia Arbuscula or as Tubastrea Coccinea. However of course these are from non-scientific sources such as forums and in some cases wetwebmedia.
So I started looking into scientific journals and came accross this article by Sentoku and Ezaki which compares the growth form and skeletal formations ofr Dendrophyllia Arbuscula and Tubastrea Coccinea. Awesome!
Coral Reefs
March 2012, Volume 31, Issue 1, pp 67-74
Regularity in budding mode and resultant growth morphology of the azooxanthellate colonial scleractinian Tubastraea coccinea
Authors: A. Sentoku, Y. Ezaki
Here is a link to the abstract and you can "peak inside" to see a diagram of the budding arrangement with respect to septa.
http://link.springer.com/article/10.1007/s00338-011-0808-5
Here is a picture from the "peak inside" that shows the budding of corallites with respect to septa in Dendrophyllia Arbuscula:
I have university access to journals so I was able to download the whole thing which was very informative. I am not sure about copy right laws pertaining to this article so I don't think I should post the other pictures from the article but they show side by side pictures of the two corals which demonstrated that coccinea has a much denser branching form where as arbuscula has a much more sparse branching form with longer branches between buddings.
They both seem to share a budding geometry in which new buds sprout from the 4 primary septa. But as I said before the overall growth form is different in terms of the length of branches.
So I am fairly convinced at this point that the coral I have is a Dendrophyllia Arbuscula. I have also looked at a piece of skeleton cross section that I took away from the base. I will see if I can take more without harming the coral to get a better view of the septa and budding cites.