A168419 a(n) = 9*floor(n/2).

0, 9, 9, 18, 18, 27, 27, 36, 36, 45, 45, 54, 54, 63, 63, 72, 72, 81, 81, 90, 90, 99, 99, 108, 108, 117, 117, 126, 126, 135, 135, 144, 144, 153, 153, 162, 162, 171, 171, 180, 180, 189, 189, 198, 198, 207, 207, 216, 216, 225, 225, 234, 234, 243, 243, 252, 252, 261

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).

Crossrefs

Cf. A004526, A017377.

Programs

Magma

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

Mathematica

Table[9 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[9 x/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 19 2013 *)
LinearRecurrence[{1,1,-1},{0,9,9},60] (* Harvey P. Dale, Apr 21 2019 *)

Formula

a(n) = 9*n - a(n-1) - 9, with n>1, a(1)=0.

G.f.: 9*x^2/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 19 2013

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

E.g.f.: (9/4)*(1 + (2*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 22 2016

Extensions

New definition by Vincenzo Librandi, Sep 19 2013