  All finite-dimensional indecomposable solvable Lie algebras $L(n,f)$, having
the triangular algebra T(n) as their nilradical, are constructed. The number of
nonnilpotent elements $f$ in $L(n,f)$ satisfies $1\leq f\leq n-1$ and the
dimension of the Lie algebra is $\dim L(n,f)=f+{1/2}n(n-1)$.
