A120848 a(n) = 2^n + 3^n - n.

2, 4, 11, 32, 93, 270, 787, 2308, 6809, 20186, 60063, 179184, 535525, 1602502, 4799339, 14381660, 43112241, 129271218, 387682615, 1162785736, 3487832957, 10462450334, 31385253891, 94151567412, 282446313673, 847322163850, 2541932937167, 7625731702688, 22877060890389

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-17,17,-6).

Formula

G.f.: (2-10*x+17*x^2-11*x^3)/((1-2*x)*(1-3*x)*(1-x)^2). - Vincenzo Librandi, Feb 06 2013

From Elmo R. Oliveira, Mar 07 2025: (Start)

E.g.f.: exp(x)*(exp(2*x) + exp(x) - x).

a(n) = 7*a(n-1) - 17*a(n-2) + 17*a(n-3) - 6*a(n-4). (End)

Mathematica

CoefficientList[Series[(2 - 10 x + 17 x^2 - 11 x^3)/((1 - 2 x) (1 - 3 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *)

Prog

(Magma) [2^n+3^n-n: n in [0..30]]; // Vincenzo Librandi, Feb 06 2013

Crossrefs

Cf. A001047, A007689.

Sequence in context: A086690 A059305 A191586 * A320567 A135339 A148170

Adjacent sequences: A120845 A120846 A120847 * A120849 A120850 A120851

Keyword

nonn,easy,changed

Author

Mohammad K. Azarian, Aug 18 2006

Extensions

Edited by Ray Chandler, Sep 06 2006

Status

approved