A120849 a(n) = 5*n + 3^n - 2^n.

0, 6, 15, 34, 85, 236, 695, 2094, 6345, 19216, 58075, 175154, 527405, 1586196, 4766655, 14316214, 42981265, 129009176, 387158435, 1161737274, 3485735925, 10458256156, 31376865415, 94134790334, 282412759385, 847255055136, 2541798719595, 7625463267394, 22876524019645

Offset

0,2

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

From Vincenzo Librandi, Feb 24 2013: (Start)

G.f.: x*(6-27*x+31*x^2)/((1-2*x)*(1-3*x)*(1-x)^2).

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

E.g.f.: exp(x)*(exp(2*x) - exp(x) + 5*x). - Elmo R. Oliveira, Mar 06 2025

Mathematica

CoefficientList[Series[x (6 - 27 x + 31 x^2)/((1-2 x) (1-3 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 24 2013 *)

Prog

(Magma) [5*n+3^n-2^n: n in [0..30]]; // Vincenzo Librandi, Feb 24 2013
(Magma) I:=[0, 6, 15, 34]; [n le 4 select I[n] else 7*Self(n-1)-17*Self(n-2)+17*Self(n-3)-6*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Feb 24 2013

Crossrefs

Cf. A001047, A007689, A008587.

Sequence in context: A350596 A232604 A332735 * A358210 A338053 A030661

Adjacent sequences: A120846 A120847 A120848 * A120850 A120851 A120852

Keyword

nonn,easy,changed

Author

Mohammad K. Azarian, Aug 18 2006

Extensions

Edited by Ray Chandler, Sep 06 2006

Status

approved