Sequence of circumscribed Cartesian coordinates

  • #1
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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?
 

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  • #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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