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A075155 Cubes of Lucas numbers. 6
8, 1, 27, 64, 343, 1331, 5832, 24389, 103823, 438976, 1860867, 7880599, 33386248, 141420761, 599077107, 2537716544, 10749963743, 45537538411, 192900170952, 817138135549, 3461452853383, 14662949322176, 62113250509227 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Mohammad K. Azarian, Identities Involving Lucas or Fibonacci and Lucas Numbers as Binomial Sums, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 45, 2012, pp. 2221-2227.

Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1).

FORMULA

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

a(n) = (-1)^n*A075151(n).

a(n) = (A000032(n))^3 = A000032(n) * A001254(n).

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

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

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

a(n) = 2*A001077(n) + 3*A061084(n+1). - R. J. Mathar, Nov 17 2011

a(n) = L(3*n) + (F(n+4) - F(n-4))*(-1)^n, n>3 and F(n)=A000045(n). - J. M. Bergot, Feb 09 2016

MAPLE

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].

MATHEMATICA

CoefficientList[Series[(8 - 23*x - 24*x^2 + x^3)/((x^2 + 4*x - 1)*(x^2 - x - 1)), {x, 0, 50}], x] (* or *) Table[LucasL[n]^3, {n, 0, 30}] (* or *) LinearRecurrence[{3, 6, -3, -1}, {8, 1, 27, 64}, 30] (* G. C. Greubel, Dec 21 2017 *)

PROG

(MAGMA) [ Lucas(n)^3 : n in [0..120]]; // Vincenzo Librandi, Apr 14 2011

(PARI) a(n)=(fibonacci(n-1)+fibonacci(n+1))^3 \\ Charles R Greathouse IV, Feb 09 2016

CROSSREFS

Cf. A000032, A061084, A075150, A075151.

Third row of array A103324.

Sequence in context: A050458 A125166 A211785 * A075151 A028943 A050311

Adjacent sequences:  A075152 A075153 A075154 * A075156 A075157 A075158

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Sep 06 2002

EXTENSIONS

Simpler definition from Ralf Stephan, Nov 01 2004

STATUS

approved

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Last modified October 20 06:43 EDT 2018. Contains 316378 sequences. (Running on oeis4.)