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

Author

Colin Barker, Jun 25 2014

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A000032, A045991, A244309.

Programs

Magma

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

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 *)

PARI

lucas(n) = if(n==0, 2, 2*fibonacci(n-1)+fibonacci(n))
vector(50, n, lucas(n-1)^3-lucas(n-1)^2)

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