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%I M3419 N1383 #28 Sep 29 2019 13:06:18
%S 1,4,11,29,54,99,163,239,344,486,648,847,1069,1355,1680,2046,2446,
%T 2911,3443,4022,4662,5395,6145,6998,7913,8913,10006,11194,12437,13751,
%U 15216,16710,18361,20123,21950,23919,25956,28150,30415,32876,35385,38049,40876
%N Number of nonnegative solutions to x^2 + y^2 + z^2 <= n^2.
%D H. Gupta, A Table of Values of N_3(t), Proc. National Institute of Sciences of India, 13 (1947), 35-63.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A000604/b000604.txt">Table of n, a(n) for n=0..500</a>
%F a(n) = [x^(n^2)] (1 + theta_3(x))^3/(8*(1 - x)), where theta_3() is the Jacobi theta function. - _Ilya Gutkovskiy_, Apr 15 2018
%t a[n_] := Sum[Boole[x^2 + y^2 + z^2 <= n^2], {x, 0, n}, {y, 0, Sqrt[n^2 - x^2]}, {z, 0, Sqrt[n^2 - x^2 - y^2]}]; A000604 = Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 100}] (* _Jean-François Alcover_, Feb 10 2016 *)
%Y Column k=3 of A302998.
%Y Cf. A000606.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_, May 22 2000
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