  We construct all solvable Lie algebras with a specific n-dimensional
nilradical n_{n,3} which contains the previously studied filiform nilpotent
algebra n_{n-2,1} as a subalgebra but not as an ideal. Rather surprisingly it
turns out that the classification of such solvable algebras can be reduced to
the classification of solvable algebras with the nilradical n_{n-2,1} together
with one additional case. Also the sets of invariants of coadjoint
representation of n_{n,3} and its solvable extensions are deduced from this
reduction. In several cases they have polynomial bases, i.e. the invariants of
the respective solvable algebra can be chosen to be Casimir invariants in its
enveloping algebra.
