A168232 a(n) = (2*n - 3*(-1)^n - 1)/2.

2, 0, 4, 2, 6, 4, 8, 6, 10, 8, 12, 10, 14, 12, 16, 14, 18, 16, 20, 18, 22, 20, 24, 22, 26, 24, 28, 26, 30, 28, 32, 30, 34, 32, 36, 34, 38, 36, 40, 38, 42, 40, 44, 42, 46, 44, 48, 46, 50, 48, 52, 50, 54, 52, 56, 54, 58, 56, 60, 58, 62, 60, 64, 62, 66, 64, 68, 66, 70, 68, 72

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

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

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

a(n) = 2*A028242(n-1). (End)

a(n) = a(n*1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 15 2013

a(n) = ceiling((n+1)/2) + floor((n+2)/2) - 4*mod(n+1,2). - Wesley Ivan Hurt, Aug 20 2014

E.g.f.: (1/2)*(-3 + 4*exp(x) + (2*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016

Sum_{n>=3} (-1)^n/a(n) = 1/2. - Amiram Eldar, Feb 25 2023

Maple

A168232:=n->n-1/2-3*(-1)^n/2: seq(A168232(n), n=1..100); # Wesley Ivan Hurt, Aug 20 2014

Mathematica

CoefficientList[Series[2 (1 + x^2 - x)/((1 + x) (x - 1)^2), {x, 0, 100}], x] (* Vincenzo Librandi, Sep 16 2013 *)
LinearRecurrence[{1, 1, -1}, {2, 0, 4}, 50] (* G. C. Greubel, Jul 16 2016 *)

Prog

(Magma) [n-1/2-3*(-1)^n/2: n in [1..60]]; // Vincenzo Librandi, Sep 16 2013
(PARI) vector(80, n, n - 1/2 - 3*(-1)^n/2) \\ Michel Marcus, Aug 21 2014

Crossrefs

Cf. A028242.

Sequence in context: A352528 A307704 A139716 * A253136 A216960 A285348

Adjacent sequences: A168229 A168230 A168231 * A168233 A168234 A168235

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 21 2009

Extensions

New definition by R. J. Mathar, Jan 05 2011

Status

approved