A168286 a(n) = (6*n + 3*(-1)^n + 1)/2.

2, 8, 8, 14, 14, 20, 20, 26, 26, 32, 32, 38, 38, 44, 44, 50, 50, 56, 56, 62, 62, 68, 68, 74, 74, 80, 80, 86, 86, 92, 92, 98, 98, 104, 104, 110, 110, 116, 116, 122, 122, 128, 128, 134, 134, 140, 140, 146, 146, 152, 152, 158, 158, 164, 164, 170, 170, 176, 176, 182, 182

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 6*n - a(n-1) - 2, with n>1, a(1)=2.

From Vincenzo Librandi, Sep 17 2013: (Start)

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

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

a(n) = 2*A168233(n) = A168301(n) + 1. (End)

E.g.f.: (1/2)*(3 - 4*exp(x) + (6*x + 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 17 2016

Mathematica

Table[3 n + 3 (-1)^n/2 + 1/2, {n, 70}] (* Bruno Berselli, Sep 17 2013 *)
CoefficientList[Series[(2 + 6 x - 2 x^2)/((1 + x) (1 - x)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *)

Prog

(Magma) [n le 1 select n+1 else 6*n-Self(n-1)-2: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013

Crossrefs

Cf. A016933, A168233, A168301.

Sequence in context: A154481 A092280 A070987 * A079458 A281914 A290378

Adjacent sequences: A168283 A168284 A168285 * A168287 A168288 A168289

Keyword

nonn,easy,less

Author

Vincenzo Librandi, Nov 22 2009

Extensions

New definition by Bruno Berselli, Sep 17 2013

Status

approved