Sequence of circumscribed Cartesian coordinates

  • #1
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
arildno
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Hmm..it was trickier than I thought to get out an explicit formula.
Nice problem! :smile:
 
  • #3
CRGreathouse
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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.
 
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  • #4
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Thanks for your alertness, both.
 

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