A168273 a(n) = 2*n + (-1)^n - 1.

0, 4, 4, 8, 8, 12, 12, 16, 16, 20, 20, 24, 24, 28, 28, 32, 32, 36, 36, 40, 40, 44, 44, 48, 48, 52, 52, 56, 56, 60, 60, 64, 64, 68, 68, 72, 72, 76, 76, 80, 80, 84, 84, 88, 88, 92, 92, 96, 96, 100, 100, 104, 104, 108, 108, 112, 112, 116, 116, 120, 120, 124, 124, 128, 128, 132

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. A052928, A008586.

Programs

Magma

[2*n-1 + (-1)^n: n in [1..70]] // Vincenzo Librandi, May 14 2013

Mathematica

CoefficientList[Series[4 x / ((1+x) (1-x)^2), {x, 0, 70}], x] (* Vincenzo Librandi, May 14 2013 *)
LinearRecurrence[{1,1,-1},{0,4,4},50] (* G. C. Greubel, Jul 16 2016 *)

PARI

a(n)=2*n-1+(-1)^n \\ Charles R Greathouse IV, Oct 07 2015

Formula

From R. J. Mathar, Jan 05 2011: (Start)

G.f.: 4*x^2/( (1+x)*(1-x)^2).

a(n) = 2*A052928(n).

a(n) = A008586(floor(n/2)). (End)

a(n) = 2*n - 2*(n mod 2). - Wesley Ivan Hurt, Jun 30 2013

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