[seqfan] count lattice points inside movable closed curve C

[Kimberling, Clark]

Seqfans,

Can someone tell a reference for problems like this:

(1)  C is a circle of fixed radius.  What are the least and greatest counts of lattice points that lie inside or on C, as C goes through all possible locations in the xy plane?
(2)  same as (1) except that C must pass through (0,0) ... or satisfy some other constraint
(3)  likewise for C a square	

In particular, in (1) take r = n and the min and max sequences to be a(n) and b(n); are they in OEIS?

Thanks.

Clark Kimberling