Buffer without overlap or slivers

[DavidLehrke]

I'm trying to automatically or quickly create a polygon feature created by buffering a line feature.  These line feature run in connected segments, the issue is I need these polygons to extend/trim so that there is no overlap or slivers between each polygon.

Notice the sliver/overlap at '61' or the gap/overlap at '62'  These are the issues I'm trying to avoid.

Another way to look at it is I want a shape similar to that created when using Copy Parallel except I want Polygons not lines.

Any help would be appreciated, thanks.

[AdCulver]

If all your buffers have the same distance you could add buffers to the points and dissolve the points and line buffers together.