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A117609
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a(n) is the number of lattice points inside or on the sphere x^2+y^2+z^2=n.
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9
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1, 7, 19, 27, 33, 57, 81, 81, 93, 123, 147, 171, 179, 203, 251, 251, 257, 305, 341, 365, 389, 437, 461, 461, 485, 515, 587, 619, 619, 691, 739, 739, 751, 799, 847, 895, 925, 949, 1021, 1021, 1045, 1141, 1189, 1213, 1237, 1309, 1357, 1357, 1365, 1419, 1503
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
S. K. K. Choi, A. V. Kumchev and R. Osburn, On sums of three squares
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FORMULA
| a(n) ~ (4/3) pi n^1.5.
a(n) = A122510(3,n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 21 2010]
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EXAMPLE
| a(2) is 19, since (0,0,0)(1 point) (0,0,1) (6 points with all rearrangements and sign assignments) and (0,1,1) (12 points) are inside or on x^2+y^2+z^2=2
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MATHEMATICA
| Table[Sum[SquaresR[3, k], {k, 0, n}], {n, 0, 50}] (* T. D. Noe, Apr 08 2006, revised Sep 27 2011 *)
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CROSSREFS
| Partial sums of A005875.
Cf. A000605 (number of points of norm <= n in cubic lattice).
Sequence in context: A014439 A175376 A175366 * A122072 A109355 A040045
Adjacent sequences: A117606 A117607 A117608 * A117610 A117611 A117612
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KEYWORD
| nonn
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AUTHOR
| John L. Drost (drost(AT)marshall.edu), Apr 06 2006
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