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A244310 a(n) = L(n)^3 - L(n)^2, where L(n) is the n-th Lucas number (A000032). 2
4, 0, 18, 48, 294, 1210, 5508, 23548, 101614, 433200, 1845738, 7840998, 33282564, 141149320, 598366458, 2535856048, 10745092894, 45524786370, 192866785668, 817050731748, 3461224027254, 14662350247600, 62111682111618, 263111844646798, 1114566304573444 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,2,-22,-4,14,-1,-1).

FORMULA

G.f.: 2*(x^6-8*x^5+17*x^4+23*x^3+5*x^2-10*x+2) / ((x+1)*(x^2-3*x+1)*(x^2-x-1)*(x^2+4*x-1)).

a(n) = A045991(A000032(n)). - Michel Marcus, Jun 25 2014

EXAMPLE

a(3) is 48 because L(3)^3 - L(3)^2 = 4^3 - 4^2 = 48.

MATHEMATICA

CoefficientList[Series[2 (x^6 - 8 x^5 + 17 x^4 + 23 x^3 + 5 x^2 - 10 x + 2)/((x + 1) (x^2 - 3 x + 1) (x^2 - x - 1) (x^2 + 4 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 26 2014 *)

Table[LucasL[n]^3 - LucasL[n]^2, {n, 0, 50}] (* G. C. Greubel, Oct 13 2018 *)

PROG

(PARI)

lucas(n) = if(n==0, 2, 2*fibonacci(n-1)+fibonacci(n))

vector(50, n, lucas(n-1)^3-lucas(n-1)^2)

(MAGMA) [Lucas(n)^3 - Lucas(n)^2: n in [0..30]]; // Vincenzo Librandi, Jun 26 2014

CROSSREFS

Cf. A000032, A045991, A244309.

Sequence in context: A302771 A167350 A215669 * A334705 A156457 A058348

Adjacent sequences:  A244307 A244308 A244309 * A244311 A244312 A244313

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jun 25 2014

STATUS

approved

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Last modified April 18 03:09 EDT 2021. Contains 343072 sequences. (Running on oeis4.)