A168193 a(n) = a(n-1) + a(n-2) + 4, with a(0)=0, a(1)=2.

0, 2, 6, 12, 22, 38, 64, 106, 174, 284, 462, 750, 1216, 1970, 3190, 5164, 8358, 13526, 21888, 35418, 57310, 92732, 150046, 242782, 392832, 635618, 1028454, 1664076, 2692534, 4356614, 7049152, 11405770, 18454926, 29860700, 48315630, 78176334, 126491968

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Formula

From R. J. Mathar, Nov 22 2009: (Start)

a(n)= 2*a(n-1) - a(n-3) = 2*A001911(n).

G.f.: 2*x*(1+x)/((x-1)*(x^2+x-1)). (End)

a(n) = a(n-1) + 2*Fibonacci(n+1), with a(0)=0. - Taras Goy, Mar 24 2019

E.g.f.: 4*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 2*sqrt(5)*sinh(sqrt(5)*x/2))/5 - 4*exp(x). - Stefano Spezia, Oct 14 2022

a(n) = A019274(n+1)+A019274(n+2). - R. J. Mathar, Jul 07 2023

Mathematica

Fibonacci[Range[3, 4! ]]*2-4 (* Vladimir Joseph Stephan Orlovsky, Mar 19 2010 *)
LinearRecurrence[{2, 0, -1}, {0, 2, 6}, 50] (* G. C. Greubel, Jul 15 2016 *)

Prog

(Magma) I:=[0, 2, 6]; [n le 3 select I[n] else Self(n-1)+Self(n-2)+4: n in [1..40]]; // Vincenzo Librandi, Jul 16 2016

Crossrefs

Sequence in context: A005819 A322072 A304627 * A182977 A116658 A210065

Adjacent sequences: A168190 A168191 A168192 * A168194 A168195 A168196

Keyword

nonn,easy

Author

Geoff Ahiakwo, Nov 19 2009

Extensions

Definition replaced by recurrence from R. J. Mathar, Nov 23 2009

Status

approved