An extremal problem concerning graphs not containing Kt and Kt,t,t

Brualdi and Mellendorf raised the following problem as a modification of Turan's theorem. Let t and n be positive integers with n>=t>=2. Determine the maximum number of edges of a graph of order n that contains neither K"t nor K"t","t as a subgraph. They solved it for n=2t (see R.A. Brualdi, S. Mellendorf, Two extremal problems in graph theory, The Electron. J. Combin. 1 (1994) #R2). We consider the following similar modification of Turan's theorem. Let t and n be positive integers with n>=t>=2. Determine the maximum number of edges of a graph of order n that contains neither K"t nor K"t","t","t as a subgraph. We solve it for n=3t.