A244310 a(n) = L(n)^3 - L(n)^2, where L(n) is the n-th Lucas number (A000032).

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

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: A378618 A167350 A215669 * A334705 A156457 A058348

Adjacent sequences: A244307 A244308 A244309 * A244311 A244312 A244313

Keyword

nonn,easy

Author

Colin Barker, Jun 25 2014

Status

approved