A168410 a(n) = 3 + 9*floor(n/2).

3, 12, 12, 21, 21, 30, 30, 39, 39, 48, 48, 57, 57, 66, 66, 75, 75, 84, 84, 93, 93, 102, 102, 111, 111, 120, 120, 129, 129, 138, 138, 147, 147, 156, 156, 165, 165, 174, 174, 183, 183, 192, 192, 201, 201, 210, 210, 219, 219, 228, 228, 237, 237, 246, 246, 255, 255

Offset: 1

Author

Vincenzo Librandi, Nov 25 2009

Keywords

• nonn
• easy
• less

Links

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

Crossrefs

Cf. A017197, A168233.

Programs

Magma

[3+9*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 19 2013

Mathematica

Table[3 + 9 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[3 (1 + 3 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 19 2013 *)

Formula

a(n) = 9*n - a(n-1) - 3, with n>1, a(1)=3.

G.f.: 3*x*(1 + 3*x - x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 10 2011

a(n) = 3*A168233(n). - R. J. Mathar, Jul 10 2011

a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 19 2013

E.g.f.: (3/4)*(3 - 4*exp(x) + (6*x + 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 21 2016

Extensions

New definition by Vincenzo Librandi, Sep 19 2013