A120845 a(n) = 2^n + 3^n + 5*n.

2, 10, 23, 50, 117, 300, 823, 2350, 6857, 20240, 60123, 179250, 535597, 1602580, 4799423, 14381750, 43112337, 129271320, 387682723, 1162785850, 3487833077, 10462450460, 31385254023, 94151567550, 282446313817, 847322164000, 2541932937323, 7625731702850, 22877060890557

Offset: 0

Author

Mohammad K. Azarian, Aug 18 2006

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A001047, A007689, A194455.

Programs

Magma

I:=[2, 10, 23, 50]; [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 26 2013

Mathematica

CoefficientList[Series[(2 - 4 x - 13 x^2 + 25 x^3)/((1-2 x) (1-3 x) (1-x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 26 2013 *)
LinearRecurrence[{7,-17,17,-6},{2,10,23,50},30] (* Harvey P. Dale, Apr 28 2016 *)

Formula

G.f.: (2-4*x-13*x^2+25*x^3)/((1-2*x)*(1-3*x)*(1-x)^2). - Bruno Berselli, Sep 01 2011

a(n) = 7*a(n-1)-17*a(n-2)+17*a(n-3)-6*a(n-4). - Vincenzo Librandi, Feb 26 2013

E.g.f.: exp(x)*(exp(x) + exp(2*x) + 5*x). - Stefano Spezia, May 06 2023

Extensions

Edited by Ray Chandler, Sep 06 2006