This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A212520 #8 Dec 11 2015 10:37:08
%S A212520 0,0,4,16,56,132,279,504,880,1380,2125,3090,4392,6006,8134,10640,
%T A212520 13824,17568,22113,27360,33700,40810,49247,58740,69696,81900,95992,
%U A212520 111384,128968,148260,169875,193440,219904,248336,280041,314262,351864,392274,436810
%N A212520 Number of (w,x,y,z) with all terms in {1,...,n} and w>=2x and y<3z.
%C A212520 For a guide to related sequences, see A211795.
%H A212520 Colin Barker, <a href="/A212520/b212520.txt">Table of n, a(n) for n = 0..1000</a>
%H A212520 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,-4,0,2,0,-2,0,4,1,-2,-2,0,1).
%F A212520 a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+ a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).
%F A212520 G.f.: x^2*(4 +16*x +48*x^2 +92*x^3 +139*x^4 +160*x^5 +178*x^6 +162*x^7 +132*x^8 +86*x^9 +46*x^10 +14*x^11 +3*x^12) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - _Colin Barker_, Dec 11 2015
%t A212520 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212520 (Do[If[w >= 2 x && y < 3 z, s = s + 1],
%t A212520 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212520 Map[t[#] &, Range[0, 50]] (* A212520 *)
%o A212520 (PARI) concat([0,0], Vec(x^2*(4 +16*x +48*x^2 +92*x^3 +139*x^4 +160*x^5 +178*x^6 +162*x^7 +132*x^8 +86*x^9 +46*x^10 +14*x^11 +3*x^12) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ _Colin Barker_, Dec 11 2015
%Y A212520 Cf. A211795, A212508.
%K A212520 nonn,easy
%O A212520 0,3
%A A212520 _Clark Kimberling_, May 20 2012