Repeated durations: pitches vs rests

[David Bellows]

The following:

{c4 16}

produces a quarter note C followed by a 16th note C

The following:

{c4 16 r4 16}

Produces a quarter C, 16th C, quarter rest, 16th C

I had hoped that the last 16th would be a rest.

This came about while trying out this code:

{c4~ 16 r4~ 16}

which produces the tie with the first two notes but again, that last
16 is a separate 16th note C.

I don't know what the expected behavior is but at least for my case,
remembering the rest would be the most helpful outcome. Or at least a
tie from a rest seems like it would always want the next note to be a
rest, right?

My music is all computer generated along with the LilyPond files and
the behavior I describe is what would be best for me, but I get if
that's not how it is for most people.

So I don't know if there is a work-around, if this is a bug, or a
feature request?

Any help would be appreciated even if it's just that my desire here is
way out of the ordinary.

Dave