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 A213488 #20 Feb 19 2024 12:10:46
%S A213488 0,1,8,27,61,113,189,295,434,609,826,1091,1407,1777,2207,2703,3268,
%T A213488 3905,4620,5419,6305,7281,8353,9527,10806,12193,13694,15315,17059,
%U A213488 18929,20931,23071,25352,27777,30352,33083,35973,39025,42245,45639
%N A213488 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| + |y-w| < w+x+y.
%C A213488 For a guide to related sequences, see A212959.
%H A213488 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-7,8,-7,4,-1).
%F A213488 a(n) = 4*a(n-1) - 7*a(n-2) + 8*a(n-3) - 7*a(n-4) + 4*a(n-5) - a(n-6).
%F A213488 G.f.: x*(1 + 4*x + 2*x^2 + x^3 + x^4)/((1 - x)^4 (1 + x^2)).
%F A213488 a(n) = (n+1)^3 - A213489(n).
%t A213488 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w + x + y > Abs[w - x] + Abs[x - y] + Abs[y - w], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A213488 m = Map[t[#] &, Range[0, 60]]
%t A213488 LinearRecurrence[{4,-7,8,-7,4,-1},{0,1,8,27,61,113},40] (* _Harvey P. Dale_, Sep 10 2019 *)
%Y A213488 Cf. A212959, A213489.
%K A213488 nonn,easy
%O A213488 0,3
%A A213488 _Clark Kimberling_, Jun 13 2012