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%I #30 Jan 01 2024 11:05:04
%S 8,-1,27,-64,343,-1331,5832,-24389,103823,-438976,1860867,-7880599,
%T 33386248,-141420761,599077107,-2537716544,10749963743,-45537538411,
%U 192900170952,-817138135549,3461452853383,-14662949322176,62113250509227,-263115950765039,1114577054530568
%N a(n)=L(n)^2*C(n), L(n)=Lucas numbers (A000032), C(n)=reflected Lucas numbers (comment to A061084).
%H Vincenzo Librandi, <a href="/A075151/b075151.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 (-3,6,3,-1).
%F a(n) = 3*L(n)+(-1)^n*L(3n).
%F a(n) = -3a(n-1)+6a(n-2)+3a(n-3)-a(n-4), n>3.
%F G.f.: ( 8+23*x-24*x^2-x^3 ) / ( (x^2+x-1)*(x^2-4*x-1) ).
%F a(n) is asymptotic to (-phi)^(3n) where phi is the golden ratio (1+sqrt(5))/2. - _Benoit Cloitre_, Sep 07 2002
%F a(n) = ((-1)^n*L(n))^3 = L(-n)^3. - _Ehren Metcalfe_, Apr 21 2018
%t CoefficientList[Series[(8+23*x-24*x^2-x^3)/(1+3*x-6*x^2-3*x^3+x^4), {x, 0, 25}], x]
%t LinearRecurrence[{-3,6,3,-1},{8,-1,27,-64},30] (* _Harvey P. Dale_, Apr 06 2013 *)
%t Table[LucasL[-n]^3, {n, 0, 25}] (* _Vincenzo Librandi_, Apr 22 2018 *)
%o (Magma) [((-1)^n*Lucas(n))^3: n in [0..30]]; // _Vincenzo Librandi_, Apr 22 2018
%Y Cf. A000032, A061084, A001254, A075155.
%K easy,sign
%O 0,1
%A Mario Catalani (mario.catalani(AT)unito.it), Sep 05 2002
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