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 A168071 #19 Oct 05 2017 20:25:37 %S A168071 1,1,-2,-5,-5,-8,-11,-11,-14,-17,-17,-20,-23,-23,-26,-29,-29,-32,-35, %T A168071 -35,-38,-41,-41,-44,-47,-47,-50,-53,-53,-56,-59,-59,-62,-65,-65,-68, %U A168071 -71,-71,-74,-77,-77,-80,-83,-83,-86,-89,-89,-92,-95,-95,-98,-101,-101,-104,-107,-107,-110,-113,-113 %N A168071 Expansion of (1-3*x^2-4*x^3)/((1-x)^2*(1+x+x^2)). %H A168071 G. C. Greubel, <a href="/A168071/b168071.txt">Table of n, a(n) for n = 0..1000</a> %H A168071 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1). %F A168071 G.f.: (1-3*x^2-4*x^3)/((1-x)^2*(1+x+x^2)). %F A168071 a(n) = A168072(n)/3^n. %F A168071 From _Wesley Ivan Hurt_, Oct 05 2017: (Start) %F A168071 a(n) = a(n-1) + a(n-3) - a(n-4) for n > 3. %F A168071 a(n) = (45 - 48*n + 18*cos(2*(n-1)*Pi/3) - 9*cos(Pi*cos(2*(n-1)*Pi/3) + Pi*sin(2*(n-1)*Pi/3)/sqrt(3)) + 14*sqrt(3)*sin(2*(n-1)*Pi/3))/24. (End) %t A168071 LinearRecurrence[{1, 0, 1, -1}, {1, 1, -2, -5}, 50] (* _G. C. Greubel_, Jul 08 2016 *) %o A168071 (PARI) Vec((1-3*x^2-4*x^3)/((1-x)^2*(1+x+x^2)) + O(x^70)) \\ _Michel Marcus_, Dec 03 2014 %Y A168071 Cf. A168053. %K A168071 easy,sign %O A168071 0,3 %A A168071 _Paul Barry_, Nov 18 2009 %E A168071 Corrected by _R. J. Mathar_, Dec 03 2014