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%I #20 Sep 08 2022 08:45:48
%S 1,3,-18,-135,-405,-1944,-8019,-24057,-91854,-334611,-1003833,
%T -3542940,-12223143,-36669429,-124357194,-416118303,-1248354909,
%U -4132485216,-13559717115,-40679151345,-132497807238,-428874481323,-1286623443969,-4142299868388
%N Expansion of (1-27x^2-108x^3)/((1-3x)^2*(1+3x+9x^2)).
%C Hankel transform of A168073.
%H G. C. Greubel, <a href="/A168072/b168072.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 (3,0,27,-81).
%F a(n) = 3^n*A168071(n).
%F a(n) = 3^n*(sin(2*Pi*n/3)/sqrt(3) - cos(2*Pi*n/3) - 2*n + 2). - _Ilya Gutkovskiy_, Jul 10 2016
%t LinearRecurrence[{3, 0, 27, -81}, {1, 3, -18, -135}, 50] (* _G. C. Greubel_, Jul 09 2016 *)
%t CoefficientList[Series[(1 - 27 x^2 - 108 x^3) / ((1 - 3 x)^2 (1 + 3 x + 9 x^2)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 10 2016 *)
%o (PARI) Vec((1-27*x^2-108*x^3)/((1-3*x)^2*(1+3*x+9*x^2)) + O(x^30)) \\ _Michel Marcus_, Dec 03 2014
%o (Magma) I:=[1,3,-18,-135]; [n le 4 select I[n] else 3*Self(n-1)+27*Self(n-3)-81*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Jul 10 2016
%Y Cf. A168071, A168073.
%K easy,sign
%O 0,2
%A _Paul Barry_, Nov 18 2009
%E Corrected by _R. J. Mathar_, Dec 03 2014
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