  In this rather computational paper, we determine certain representation
numbers of ideals in real quadratic number fields explicitly in order to obtain
a representation of the associated Dirichlet series in terms of Dirichlet
L-functions and a generalized divisor sum. A direct and important consequence
is that the Dirichlet series has a meromorphic continuation to the whole
complex plane and a simple pole at $s=2$ whose residue can be made explicit in
terms of the Dirichlet L-functions and the generalized divisor sum.
