  In this work the role of magnetic Landau quantization in the dynamics and
spectrum of Diced Lattice charge carriers is studied in terms of the associated
pseudospin 1 Green's function. The equations of motion for the 9 matrix
elements of this Green's function are formulated in position/frequency
representation and are solved explicitly in terms of a closed form integral
representation involving only elementary functions. The latter is subsequently
expanded in a Laguerre eigenfunction series whose frequency poles identify the
discretized energy spectrum for the Landau-quantized Diced Lattice as
$\epsilon_n = \pm\sqrt{2(2n+1)\alpha^2 eB}$ ($\alpha\sqrt{2}$ is the
characteristic speed for the Diced Lattice) which differs significantly from
the nonrelativistic linear dependence of $\epsilon_n$ on $B$, and is similar to
the corresponding $\sqrt{B}-$dependence of other Dirac materials (Graphene,
Group VI Dichalcogenides).
