Sequence of circumscribed Cartesian coordinates

1. Feb 24, 2007

Loren Booda

What is the sequence described by the counts of integer Cartesian coordinates (x, y) within circles of successive whole number radii centered at the origin?

2. Feb 24, 2007

arildno

Hmm..it was trickier than I thought to get out an explicit formula.
Nice problem!

3. Feb 24, 2007

CRGreathouse

It's the Gauss Circle Problem, with values http://www.research.att.com/~njas/sequences/A000328 [Broken] or http://www.research.att.com/~njas/sequences/A051132 [Broken] depending on how you handle the boundaries. I don't have an explicit formula for this myself, though the MathWorld article has a few sum representations.

Last edited by a moderator: May 2, 2017
4. Feb 24, 2007