A168202 a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=5.

5, 2, 8, 5, 11, 8, 14, 11, 17, 14, 20, 17, 23, 20, 26, 23, 29, 26, 32, 29, 35, 32, 38, 35, 41, 38, 44, 41, 47, 44, 50, 47, 53, 50, 56, 53, 59, 56, 62, 59, 65, 62, 68, 65, 71, 68, 74, 71, 77, 74, 80, 77, 83, 80, 86, 83, 89, 86, 92, 89, 95, 92, 98, 95, 101, 98, 104, 101, 107, 104

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

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

a(n) = a(n-1) + a(n-2) - a(n-3).

a(n) = (5 - 9*(-1)^n)/4 + 3*n/2.

G.f.: x*(5 - 3*x + x^2)/((1+x)*(x-1)^2). (End)

E.g.f.: (1/4)*(-9 + 4*exp(x) + (5 + 6*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016

Sum_{n>=1} (-1)^n/a(n) = 1/2. - Amiram Eldar, Feb 23 2023

Mathematica

LinearRecurrence[{1, 1, -1}, {5, 2, 8}, 60] (* Vincenzo Librandi, Feb 28 2012 *)

Prog

(Magma) I:=[5, 2, 8]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 28 2012

Crossrefs

Sequence in context: A185353 A345712 A355972 * A153455 A193019 A200135

Adjacent sequences: A168199 A168200 A168201 * A168203 A168204 A168205

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 20 2009

Status

approved