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