cp's OEIS Frontend

A211639 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2+x^2+y^2<=n.

%I A211639 #16 Oct 23 2024 08:40:37
%S A211639 0,0,0,1,1,1,4,4,4,7,7,10,11,11,17,17,17,20,23,26,26,32,35,35,38,38,
%T A211639 44,48,48,54,60,60,60,66,69,75,78,78,87,87,87,96,102,105,108,114,120,
%U A211639 120,121,127,133,139,139,145,157,157,163,169,169,178,178,184,196
%N A211639 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2+x^2+y^2<=n.
%C A211639 For a guide to related sequences, see A211422.
%F A211639 a(n) = A211638(n)+A063691(n). - _R. J. Mathar_, Jan 07 2015
%F A211639 G.f.: (theta_3(x) - 1)^3/(8*(1 - x)), where theta_3() is the Jacobi theta function. - _Ilya Gutkovskiy_, Apr 17 2018
%t A211639 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A211639     (Do[If[w^2 + x^2 + y^2 <= n, s = s + 1],
%t A211639         {w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
%t A211639 Map[t[#] &, Range[0, 80]]     (* A211639 *)
%t A211639 (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y A211639 Cf. A211638, A211422. Partial sums of A063691.
%K A211639 nonn
%O A211639 0,7
%A A211639 _Clark Kimberling_, Apr 18 2012