%I #14 Oct 01 2016 04:34:39
%S 4,-1,9,-16,49,-121,324,-841,2209,-5776,15129,-39601,103684,-271441,
%T 710649,-1860496,4870849,-12752041,33385284,-87403801,228826129,
%U -599074576,1568397609,-4106118241,10749957124,-28143753121,73681302249,-192900153616,505019158609,-1322157322201
%N a(n)=L(n)*C(n), L(n)=Lucas numbers (A000032), C(n)=reflected Lucas numbers (see comment to A061084).
%H Colin Barker, <a href="/A075150/b075150.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,2,1).
%F a(n) = 2+(-1)^n*L(2n).
%F a(n) = -2a(n-1)+2a(n-2)+a(n-3) with a(0)=4, a(1)=-1, a(2)=9.
%F G.f.: (4 + 7*x - x^2)/(1 + 2*x - 2*x^2 - x^3).
%F a(n) = (-1)^n*A001254(n). - _R. J. Mathar_, Jan 11 2012
%F a(n) = (2+(1/2*(-3-sqrt(5)))^n+(1/2*(-3+sqrt(5)))^n). - _Colin Barker_, Oct 01 2016
%t CoefficientList[Series[(4 + 7*x - x^2)/(1 + 2*x - 2*x^2 - x^3), {x, 0, 30}], x]
%t LinearRecurrence[{-2,2,1},{4,-1,9},50] (* _Harvey P. Dale_, Nov 08 2011 *)
%o (PARI) a(n) = round((2+(1/2*(-3-sqrt(5)))^n+(1/2*(-3+sqrt(5)))^n)) \\ _Colin Barker_, Oct 01 2016
%o (PARI) Vec((4+7*x-x^2)/(1+2*x-2*x^2-x^3) + O(x^30)) \\ _Colin Barker_, Oct 01 2016
%Y Cf. A000032, A061084.
%K easy,sign
%O 0,1
%A Mario Catalani (mario.catalani(AT)unito.it), Sep 05 2002