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Search: id:A002102
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| A002102 |
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Number of nonnegative solutions to x^2 + y^2 + z^2 = n.
(Formerly M2265 N0895)
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+0
2
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| 1, 3, 3, 1, 3, 6, 3, 0, 3, 6, 6, 3, 1, 6, 6, 0, 3, 9, 6, 3, 6, 6, 3, 0, 3, 9, 12, 4, 0, 12, 6, 0, 3, 6, 9, 6, 6, 6, 9, 0, 6, 15, 6, 3, 3, 12, 6, 0, 1, 9, 15, 6, 6, 12, 12, 0, 6, 6, 6, 9, 0, 12, 12, 0, 3, 18, 12, 3, 9, 12, 6, 0, 6, 9, 18, 7, 3, 12, 6, 0, 6, 15, 9, 9, 6, 12, 15, 0, 3, 21, 18, 6, 0, 6
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
H. Gupta, A Table of Values of N_3(t), Proc. National Institute of Sciences of India, 13 (1947), 35-63.
A. Das and A. C. Melissinos, Quantum Mechanics: A Modern Introduction, Gordon and Breach, 1986, p. 48.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
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FORMULA
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Coefficient of q^k in 1/8*(1 + theta_3(0, q))^3, or coefficient of q^n in (1+q+q^4+q^9+q^16+q^25+q^36+q^49+q^64+...)^3.
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MATHEMATICA
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a[n_] := Module[{x, y, z, c}, For[x=c=0, x^2<=n, x++, For[y=0, x^2+y^2<=n, y++, If[IntegerQ[Sqrt[n-x^2-y^2]], c++ ]]]; c]
CoefficientList[Series[Sum[q^n^2, {n, 0, 12}], {q, 0, 150}]^3, q]
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CROSSREFS
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More terms from Dean Hickerson, Oct 07, 2001
First differences of A000606.
Sequence in context: A109630 A080094 A002332 this_sequence A047655 A078685 A078882
Adjacent sequences: A002099 A002100 A002101 this_sequence A002103 A002104 A002105
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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