User blog comment:SuperSpruce/The T array function/@comment-38080588-20190221190022

I am not exactly sure how you evaluate this function, but it looks to me like \(TT(n)\) would be around \(f_{\varphi(\omega,0)}(n)\) assuming your analysis is correct and the pattern it is showing continues as shown. However, I am not sure that your analysis is correct. It would be easier to analyze if you explained what \(T_{n+1}(n)\) and other different subscripts do, because that is the main thing that seems missing from your definition of the function, making it impossible to analyze, for example when you showed "\(T_{(T_n[a-1])}[a-1]\)".