how to construct lod based on quadtree

i am a student who are studying Lindstrom
's paper about constructing LOD for large terrain(sigraph 96), i want to use quadtree to construct real-time,continuous lod of heightfields based on his algorithm,but there are some problems puzzled me.
in his paper, i found the oringal data is (2^n+1)(2^n+1),but the most data we can use are (2^n)(2^n),so how can we do ?
i think interpolation is a uncomfortable way.
i am anxiousely waiting for your help, thank you very much!