Search: id:A002102
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%I A002102 M2265 N0895
%S A002102 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,
%T A002102 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,
%U A002102 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
%N A002102 Number of nonnegative solutions to x^2 + y^2 + z^2 = n.
%D A002102 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002102 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002102 H. Gupta, A Table of Values of N_3(t), Proc. National Institute of Sciences 
               of India, 13 (1947), 35-63.
%D A002102 A. Das and A. C. Melissinos, Quantum Mechanics: A Modern Introduction, 
               Gordon and Breach, 1986, p. 48.
%H A002102 T. D. Noe, <a href="b002102.txt">Table of n, a(n) for n=0..10000</a>
%F A002102 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.
%t A002102 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]
%t A002102 CoefficientList[Series[Sum[q^n^2, {n, 0, 12}], {q, 0, 150}]^3, q]
%Y A002102 More terms from Dean Hickerson, Oct 07, 2001
%Y A002102 First differences of A000606.
%Y A002102 Sequence in context: A109630 A080094 A002332 this_sequence A047655 A078685 
               A078882
%Y A002102 Adjacent sequences: A002099 A002100 A002101 this_sequence A002103 A002104 
               A002105
%K A002102 nonn
%O A002102 0,2
%A A002102 N. J. A. Sloane (njas(AT)research.att.com).

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