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 A211615 #12 Dec 04 2016 19:46:27 %S A211615 0,6,24,60,114,186,276,384,510,654,816,996,1194,1410,1644,1896,2166, %T A211615 2454,2760,3084,3426,3786,4164,4560,4974,5406,5856,6324,6810,7314, %U A211615 7836,8376,8934,9510,10104,10716,11346,11994,12660,13344,14046 %N A211615 Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and -1<=w+x+y<=1. %C A211615 For a guide to related sequences, see A211422. %H A211615 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1). %F A211615 a(n)= 6*A005448(n). %F A211615 a(n) = 3a(n-1)-3a(n-2)+a(n-3) for n>3. %F A211615 a(n) = 6-9*n+9*n^2 for n>0. G.f.: 6*x*(1+x+x^2)/(1-x)^3. [_Colin Barker_, Sep 09 2012] %t A211615 t = Compile[{{u, _Integer}}, Module[{s = 0}, (Do[If[-1 <= w + x + y <= 1, s = s + 1], {w, #}, {x, #}, {y, #}] &[Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]]; %t A211615 Map[t[#] &, Range[0, 70]] (* A211615 *) %t A211615 %/6 (* A005448 *) %t A211615 FindLinearRecurrence[%] %t A211615 (* _Peter J. C. Moses_, Apr 13 2012 *) %t A211615 Join[{0},LinearRecurrence[{3, -3, 1},{6, 24, 60},40]] (* _Ray Chandler_, Aug 02 2015 *) %Y A211615 Cf. A211422. %K A211615 nonn,easy %O A211615 0,2 %A A211615 _Clark Kimberling_, Apr 16 2012