A168381 a(n) = 4*n + 2*(-1)^n.

2, 10, 10, 18, 18, 26, 26, 34, 34, 42, 42, 50, 50, 58, 58, 66, 66, 74, 74, 82, 82, 90, 90, 98, 98, 106, 106, 114, 114, 122, 122, 130, 130, 138, 138, 146, 146, 154, 154, 162, 162, 170, 170, 178, 178, 186, 186, 194, 194, 202, 202, 210, 210, 218, 218, 226, 226, 234, 234

Offset: 1

Author

Vincenzo Librandi, Nov 24 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. A163980.

Programs

Magma

[4*n +2*(-1)^n: n in [1..70]]; // Vincenzo Librandi, Sep 18 2013

Mathematica

CoefficientList[Series[(2 + 8 x - 2 x^2)/((1 + x) (x -1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)

Formula

a(n) = 8*n - a(n-1) - 4, with n>1, a(1)=2.

G.f.: 2*x*(1 + 4*x - x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 18 2013

a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 18 2013

From Bruno Berselli, Sep 18 2013: (Start)

a(n) = 2*A163980(n).

a(n) = 2 + 8*floor(n/2). (End)

E.g.f.: 2*(1 - exp(x) + 2*x*exp(2*x))*exp(-x). - G. C. Greubel, Jul 19 2016

Extensions

Definition rewritten by Vincenzo Librandi, Sep 18 2013