%I #21 Sep 08 2022 08:45:37
%S -3,0,27,-18,-63,36,207,-126,-603,360,1827,-1098,-5463,3276,16407,
%T -9846,-49203,29520,147627,-88578,-442863,265716,1328607,-797166,
%U -3985803,2391480,11957427,-7174458,-35872263,21523356,107616807,-64570086,-322850403,193710240
%N Expansion of 3*x*(3*x+1)*(2*x-1) / ( (1+x)*(3*x^2+1) ).
%C All entries are multiples of 3.
%H Vincenzo Librandi, <a href="/A143769/b143769.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-3,-3)
%F a(n) = A141533(n+1)-2*A141533(n).
%F a(2n)+a(2n+1) = (-1)^n*A000244(n).
%F a(n) = (3/2) * ((2*(-1)^n - 3) * (-3)^floor(n/2) - 3*(-1)^n ). - _Ralf Stephan_, Aug 17 2013
%t CoefficientList[Series[3 (3 x + 1) (2 x - 1) / ((1 + x) (3 x^2 + 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 17 2013 *)
%t LinearRecurrence[{-1,-3,-3},{-3,0,27},40] (* _Harvey P. Dale_, Dec 26 2014 *)
%o (PARI) a(n)=3/2*((2*(-1)^n-3)*(-3)^floor(n/2)-3*(-1)^n); \\ _Ralf Stephan_, Aug 17 2013
%o (Magma) I:=[-3,0,27]; [n le 3 select I[n] else -Self(n-1)-3*Self(n-2) -3*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Aug 17 2013
%K sign,easy
%O 1,1
%A _Paul Curtz_, Aug 31 2008