input box width, box length, and plate radius:
box width=4.000000, box length=4.000000, and plate radius=0.500000:
dense packing = 14
grid packing = 16
(0,0) has 5 on top.
(0,1) has 8 on top.
(0,2) has 8 on top.
(0,3) has 5 on top.