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A075151 a(n)=L(n)^2*C(n), L(n)=Lucas numbers (A000032), C(n)=reflected Lucas numbers (comment to A061084). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

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) = [ -2+sqrt(5)]^n+3*[1/2+(1/2)*sqrt(5)]^n+[ -2-sqrt(5)]^n+3*[1/2-(1/2)*sqrt(5)]^n, with n>=0 - Paolo P. Lava, Jun 12 2008

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

PROG

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

CROSSREFS

Cf. A000032, A061084, A001254, A075155.

Sequence in context: A125166 A211785 A075155 * A028943 A050311 A224997

Adjacent sequences:  A075148 A075149 A075150 * A075152 A075153 A075154

KEYWORD

easy,sign

AUTHOR

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

STATUS

approved

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Last modified February 29 03:43 EST 2020. Contains 332353 sequences. (Running on oeis4.)