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A224212 Number of nonnegative solutions to x^2 + y^2 <= n.

%I A224212 #15 Mar 24 2021 09:52:24
%S A224212 1,3,4,4,6,8,8,8,9,11,13,13,13,15,15,15,17,19,20,20,22,22,22,22,22,26,
%T A224212 28,28,28,30,30,30,31,31,33,33,35,37,37,37,39,41,41,41,41,43,43,43,43,
%U A224212 45,48,48,50,52,52,52,52,52,54,54,54,56,56,56,58,62,62,62,64
%N A224212 Number of nonnegative solutions to x^2 + y^2 <= n.
%H A224212 Seiichi Manyama, <a href="/A224212/b224212.txt">Table of n, a(n) for n = 0..1000</a>
%F A224212 G.f.: (1/(1 - x))*(Sum_{k>=0} x^(k^2))^2. - _Ilya Gutkovskiy_, Mar 14 2017
%t A224212 nn = 68; t = Table[0, {nn}]; Do[d = x^2 + y^2; If[0 < d <= nn, t[[d]]++], {x, 0, nn}, {y, 0, nn}]; Accumulate[Join[{1}, t]] (* _T. D. Noe_, Apr 01 2013 *)
%o A224212 (Python)
%o A224212 for n in range(99):
%o A224212   k = 0
%o A224212   for x in range(99):
%o A224212     s = x*x
%o A224212     if s>n: break
%o A224212     for y in range(99):
%o A224212         sy = s + y*y
%o A224212         if sy>n: break
%o A224212         k+=1
%o A224212   print(str(k), end=', ')
%Y A224212 Cf. A000925 (first differences).
%Y A224212 Cf. A000606 (number of nonnegative solutions to x^2 + y^2 + z^2 <= n).
%Y A224212 Cf. A057655 (number of integer solutions to x^2 + y^2 <= n).
%K A224212 nonn
%O A224212 0,2
%A A224212 _Alex Ratushnyak_, Apr 01 2013