Sequence of circumscribed Cartesian coordinates

[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?

 

[arildno]

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

 

[CRGreathouse]

It's the Gauss Circle Problem, with values http://www.research.att.com/~njas/sequences/A000328 or http://www.research.att.com/~njas/sequences/A051132 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.

 

[Loren Booda]

Thanks for your alertness, both.