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Search: id:A117609
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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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+0
5
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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; listen)
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OFFSET
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0,2
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COMMENT
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a(n) should be approximately (4/3) pi n^1.5, how good is this approximation?
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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EXAMPLE
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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
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Needs["NumberTheory`NumberTheoryFunctions`"]; Table[Sum[SumOfSquaresR[3, k], {k, 0, n}], {n, 0, 50}] - T. D. Noe (noe(AT)sspectra.com), Apr 08 2006
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CROSSREFS
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Cf. A000605 (number of points of norm <= n in cubic lattice).
Sequence in context: A006063 A038593 A014439 this_sequence A122072 A109355 A040045
Adjacent sequences: A117606 A117607 A117608 this_sequence A117610 A117611 A117612
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KEYWORD
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nonn
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AUTHOR
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John L. Drost (drost(AT)marshall.edu), Apr 06 2006
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