  A previous mathematical approach adopted for optimizing the number of total
device elements required for obtaining high effective quantized resistances in
graphene-based quantum Hall array devices (QHARS) has been further explored
with partial recursion patterns. Designs would assume the use of epitaxial
graphene elements, whose quantized Hall resistance at the {\nu}=2 plateau (R_H
\approx 12906.4 \Ohm) becomes the building block for larger effective,
quantized resistances. Auxiliary calculations suggest the importance of
applying full recursions at least once to maximize the reduction of total QHARS
elements needed for high resistances.
