A168276 a(n) = 2*n - (-1)^n - 1.

2, 2, 6, 6, 10, 10, 14, 14, 18, 18, 22, 22, 26, 26, 30, 30, 34, 34, 38, 38, 42, 42, 46, 46, 50, 50, 54, 54, 58, 58, 62, 62, 66, 66, 70, 70, 74, 74, 78, 78, 82, 82, 86, 86, 90, 90, 94, 94, 98, 98, 102, 102, 106, 106, 110, 110, 114, 114, 118, 118, 122, 122, 126, 126, 130, 130

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).

Crossrefs

Cf. A039722, A168277.

Cf. A063210. - R. J. Mathar, Nov 25 2009

Programs

Magma

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

Mathematica

CoefficientList[Series[2 (1 + x^2) / ((1 + x) (1 - x)^2), {x, 0, 80}], x] (* Vincenzo Librandi, Sep 16 2013 *)
Table[2 n - 1 - (-1)^n, {n, 70}] (* Bruno Berselli, Sep 17 2013 *)
LinearRecurrence[{1,1,-1},{2,2,6},70] (* Harvey P. Dale, Oct 22 2014 *)

Formula

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

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

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

a(n) = 2*A109613(n-1).

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

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

a(n) = A168277(n) + 1. - Vincenzo Librandi, Sep 17 2013

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

Sum_{n>=1} 1/a(n)^2 = Pi^2/16. - Amiram Eldar, Aug 21 2022

Extensions

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