A075151 a(n)=L(n)^2*C(n), L(n)=Lucas numbers (A000032), C(n)=reflected Lucas numbers (comment to A061084).

8, -1, 27, -64, 343, -1331, 5832, -24389, 103823, -438976, 1860867, -7880599, 33386248, -141420761, 599077107, -2537716544, 10749963743, -45537538411, 192900170952, -817138135549, 3461452853383, -14662949322176, 62113250509227, -263115950765039, 1114577054530568

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 05 2002

Keywords

• easy
• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-3,6,3,-1).

Crossrefs

Cf. A000032, A061084, A001254, A075155.

Programs

Magma

[((-1)^n*Lucas(n))^3: n in [0..30]]; // Vincenzo Librandi, Apr 22 2018

Mathematica

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]
LinearRecurrence[{-3,6,3,-1},{8,-1,27,-64},30] (* Harvey P. Dale, Apr 06 2013 *)
Table[LucasL[-n]^3, {n, 0, 25}] (* Vincenzo Librandi, Apr 22 2018 *)

Formula

a(n) = 3*L(n)+(-1)^n*L(3n).

a(n) = -3a(n-1)+6a(n-2)+3a(n-3)-a(n-4), n>3.

G.f.: ( 8+23*x-24*x^2-x^3 ) / ( (x^2+x-1)*(x^2-4*x-1) ).

a(n) is asymptotic to (-phi)^(3n) where phi is the golden ratio (1+sqrt(5))/2. - Benoit Cloitre, Sep 07 2002

a(n) = ((-1)^n*L(n))^3 = L(-n)^3. - Ehren Metcalfe, Apr 21 2018