A168283 a(n) = (10*n - 5*(-1)^n - 3)/4.

3, 3, 8, 8, 13, 13, 18, 18, 23, 23, 28, 28, 33, 33, 38, 38, 43, 43, 48, 48, 53, 53, 58, 58, 63, 63, 68, 68, 73, 73, 78, 78, 83, 83, 88, 88, 93, 93, 98, 98, 103, 103, 108, 108, 113, 113, 118, 118, 123, 123, 128, 128, 133, 133, 138, 138, 143, 143, 148, 148, 153, 153, 158

Offset: 1

Author

Vincenzo Librandi, Nov 22 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

[n le 1 select n+2 else 5*n-Self(n-1)-4: n in [1..70] ]; // Vincenzo Librandi, Sep 16 2013

Mathematica

CoefficientList[Series[(3 + 2 x^2) / ((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 16 2013 *)
Table[5 n/2 - 5 (-1)^n/4 - 3/4, {n, 70}] (* Bruno Berselli, Sep 17 2013 *)

Formula

a(n) = 5*n - a(n-1) - 4, with n>1, a(1)=3.

From R. J. Mathar, Nov 25 2009: (Start)

a(n) = A168209(n-1), n>1.

a(n) = (10*n + 5*(-1)^(n+1) - 3)/4.

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

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

E.g.f.: (1/4)*(-5 + 8*exp(x) + (10*x - 3)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 17 2016

Extensions

Previous definition replaced with the closed form by Bruno Berselli, Sep 17 2013