  The famous linear diophantine problem of Frobenius is the problem to
determine the largest integer (Frobenius number) whose number of
representations in terms of $a_1,\dots,a_k$ is at most zero, that is not
representable. In other words, all the integers greater than this number can be
represented for at least one way. One of the natural generalizations of this
problem is to find the largest integer (generalized Frobenius number) whose
number of representations is at most a given nonnegative integer $p$. It is
easy to find the explicit form of this number in the case of two variables.
However, no explicit form has been known even in any special case of three
variables. In this paper we are successful to show explicit forms of the
generalized Frobenius numbers of the triples of triangular numbers. When $p=0$,
their Frobenius number is given by Robles-P\'erez and Rosales in 2018.
