A168384 a(n) = 4*n - 2*(-1)^n.

6, 6, 14, 14, 22, 22, 30, 30, 38, 38, 46, 46, 54, 54, 62, 62, 70, 70, 78, 78, 86, 86, 94, 94, 102, 102, 110, 110, 118, 118, 126, 126, 134, 134, 142, 142, 150, 150, 158, 158, 166, 166, 174, 174, 182, 182, 190, 190, 198, 198, 206, 206, 214, 214, 222, 222, 230, 230

Offset: 1

Author

Vincenzo Librandi, Nov 24 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. A296910.

Programs

Magma

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

Magma

[6+8*Floor((n-1)/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013

Mathematica

CoefficientList[Series[(6 + 2 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)
LinearRecurrence[{1,1,-1},{6,6,14},70] (* Harvey P. Dale, Mar 14 2023 *)

Formula

a(n) = 8*n - a(n-1) - 4, with n>1, a(1)=6.

From Vincenzo Librandi, Sep 18 2013: (Start)

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

a(n) = a(n-1) + a(n-2) - a(n-3).

a(n) = 6 + 8*floor((n-1)/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