First, another way of thinking about a 1x16 display (1/16 duty) is that the first 8 characters are on line 1 and the second 8 characters are on line 2, even though the device has one line.
For the OPTEX DMC-16202NY 2x16 display (1/16 duty), the DD RAM addresses are:
DD Ram Addresses Starting Address Command Line 1 00 to 0F 0x80 Line 2 40 to 4F 0xC0
With this in mind, the LCD code in "PIC'n Up The Pace" or "Microcontrol'n Apps" can be modified easily to work with the DMC-162092, and then expanded to suit your needs.