[seqfan] Re: count lattice points inside movable closed curve C

Neil Sloane njasloane at gmail.com
Fri Jun 7 21:50:09 CEST 2013


My paper with Teo,

Theta Series and Magic Numbers for Close-Packed Spherical Clusters

http://neilsloane.com/doc/magic2/magic2.html

has some tables related to this question.

By the way, the answers are likely to be nicer if one sets the squared
radius to be n

Neil


On Fri, Jun 7, 2013 at 3:40 PM, Kimberling, Clark <ck6 at evansville.edu>wrote:

> 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
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


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