A168236 a(n) = (6*n - 3*(-1)^n - 1)/4.

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

Offset: 1

Author

Vincenzo Librandi, Nov 21 2009

Keywords

• nonn
• easy
• less

Comments

Essentially the same as A168199. - Georg Fischer, Oct 14 2018

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. A016789.

Programs

Magma

[3*n/2-1/4-3*(-1)^n/4: n in [1..70]]; // Vincenzo Librandi, Sep 16 2013

Mathematica

CoefficientList[Series[(2 + x^2) / ((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 16 2013 *)
Table[(6*n - 3*(-1)^n - 1)/4, {n,1,50}] (* or *) LinearRecurrence[ {1,1, -1}, {2, 2, 5}, 50] (* G. C. Greubel, Jul 16 2016 *)

Formula

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

a(n+1) = A016789(floor(n/2)).

a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 16 2013

E.g.f.: (1/4)*(-3 + 4*exp(x) + (6*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016