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Search: id:A014465
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| A014465 |
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Let b(n) = n-th number of form x^2+y^2+z^2, x,y,z >= 1 (A000408); a(n) = number of solutions (x,y,z) to x^2+y^2+z^2=b(n). |
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+0
1
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| 1, 3, 3, 3, 1, 6, 3, 3, 3, 6, 3, 3, 6, 4, 6, 6
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The a(n) are also the degeneracies of the energy levels E(n) in the three dimensional cubic "particle-in-a-box" model in elementary quantum mechanics. [From Tim Royappa (royappa(AT)uwf.edu), Jan 09 2009]
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REFERENCES
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G. M. Barrow, Physical Chemistry (6th ed.), McGraw-Hill, 1996, p. 69. [From Tim Royappa (royappa(AT)uwf.edu), Jan 09 2009]
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EXAMPLE
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b(1) = 3 = 1^2+1^2+1^2 (1 way), so a(1) = 1; b(2) = 6 = 2^2+1^2+1^2 (3 ways), so a(2) = 3; etc.
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CROSSREFS
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Sequence in context: A123073 A059289 A163644 this_sequence A155969 A076237 A128210
Adjacent sequences: A014462 A014463 A014464 this_sequence A014466 A014467 A014468
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KEYWORD
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nonn,easy
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AUTHOR
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Tim Royappa (royappa(AT)uwf.edu), 1997; entry revised Jun 13, 2003.
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