A168414 a(n) = (18*n - 9*(-1)^n - 3)/4.

6, 6, 15, 15, 24, 24, 33, 33, 42, 42, 51, 51, 60, 60, 69, 69, 78, 78, 87, 87, 96, 96, 105, 105, 114, 114, 123, 123, 132, 132, 141, 141, 150, 150, 159, 159, 168, 168, 177, 177, 186, 186, 195, 195, 204, 204, 213, 213, 222, 222, 231, 231, 240, 240, 249, 249, 258

Offset: 1

Author

Vincenzo Librandi, Nov 25 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Magma

[6+9*Floor((n-1)/2): n in [1..70]]; // Vincenzo Librandi, Sep 19 2013

Mathematica

Table[6 + 9 Floor[(n - 1)/2], {n, 70}] (* or *) CoefficientList[Series[3 (2 + x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 19 2013 *)
LinearRecurrence[{1,1,-1},{6,6,15},60] (* Harvey P. Dale, May 17 2017 *)

Formula

a(n) = 9*n - a(n-1) - 6, n>1.

From R. J. Mathar, Jul 10 2011: (Start)

a(n) = 3*A168236(n).

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

a(n) = 6 + 9*Floor((n-1)/2). - Vincenzo Librandi, Sep 19 2013

From G. C. Greubel, Jul 22 2016: (Start)

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

E.g.f.: (3/4)*(-3 + 4*exp(x) +(6*x - 1)*exp(2*x))*exp(-x). (End)

Extensions

Definition replaced by Lava formula of Nov 2009. - R. J. Mathar, Jul 10 2011