To look at it visually, here is the layout of a typical ahnentafel chart, with the mathmatical numbering system illustrated:
1. person
2. father (1*2)
3. mother (1*2+1)
4. paternal grandfather (2*2)
5. paternal grandmother (2*2+1)
6. maternal grandfather (4*2)
7. maternal grandmother (4*2+1)
8. paternal grandfather's father - great grandfather (4*2)
9. paternal grandfather's mother - great grandmother (4*2+1)
10. paternal grandmother's father - great grandfather (5*2)
11. paternal grandmother's mother - great grandmother (5*2+1)
12. maternal grandfather's father - great grandfather (6*2)
13. maternal grandfather's mother - great grandmother (6*2+1)
14. maternal grandmother's father - great grandfather (7*2)
15. maternal grandmother's mother - great grandmother (7*2+1)
You may notice that the numbers used here are exactly the same as you're used to seeing in a pedigree chart. It is just presented in a more condensed, list format. Unlike the brief example shown here, a true ahnentafel will list each individual's full name, and dates and places of birth, marriage and death (if known).
You can create an ahnentafel chart by hand or produce it with your genealogy software program (where you may see it referred to as an ancestor chart. The ahnentafel is great for sharing because it only lists direct line ancestors, and presents them in a compact format that is easy to read.

