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A000606 Number of nonnegative solutions to x^2 + y^2 + z^2 <= n.

%I A000606 M3294 N1329 #38 Feb 01 2022 01:04:15
%S A000606 1,4,7,8,11,17,20,20,23,29,35,38,39,45,51,51,54,63,69,72,78,84,87,87,
%T A000606 90,99,111,115,115,127,133,133,136,142,151,157,163,169,178,178,184,
%U A000606 199,205,208,211,223,229,229,230,239,254,260,266,278,290,290,296
%N A000606 Number of nonnegative solutions to x^2 + y^2 + z^2 <= n.
%D A000606 H. Gupta, A Table of Values of N_3(t), Proc. National Institute of Sciences of India, 13 (1947), 35-63.
%D A000606 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000606 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000606 T. D. Noe, <a href="/A000606/b000606.txt">Table of n, a(n) for n = 0..1000</a>
%F A000606 G.f.: (1/(1 - x))*(Sum_{k>=0} x^(k^2))^3. - _Ilya Gutkovskiy_, Mar 14 2017
%t A000606 nn = 50; t = Table[0, {nn}]; Do[d = x^2 + y^2 + z^2; If[0 < d <= nn, t[[d]]++], {x, 0, nn}, {y, 0, nn}, {z, 0, nn}]; Accumulate[Join[{1}, t]] (* _T. D. Noe_, Apr 01 2013 *)
%o A000606 (Python)
%o A000606 for n in range(99):
%o A000606   k = 0
%o A000606   for x in range(99):
%o A000606     s = x*x
%o A000606     if s > n: break
%o A000606     for y in range(99):
%o A000606         sy = s + y*y
%o A000606         if sy > n: break
%o A000606         for z in range(99):
%o A000606             sz = sy + z*z
%o A000606             if sz > n: break
%o A000606             k += 1
%o A000606   print(str(k), end=',')
%o A000606 # _Alex Ratushnyak_, Apr 01 2013
%Y A000606 Cf. A000604, A117609.
%Y A000606 Cf. A002102 (first differences).
%K A000606 nonn
%O A000606 0,2
%A A000606 _N. J. A. Sloane_
%E A000606 More terms from _Sean A. Irvine_, Dec 01 2010