A168237 a(n) = (6*n + 3*(-1)^n - 3)/4.

0, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 69, 69, 72, 72, 75, 75, 78, 78, 81, 81, 84, 84, 87, 87, 90, 90, 93, 93, 96, 96, 99, 99, 102, 102, 105, 105

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000 [a(0)=0 added by Georg Fischer, Feb 02 2021]

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

Formula

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

a(n) = 3*A110654(n-1) for n >= 1.

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

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

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

a(n) = 3*floor(n/2). - Daniel Checa, Mar 10 2024

Mathematica

CoefficientList[Series[3*x^2/((1 + x)*(x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 16 2013 *)
Table[(6*n + 3*(-1)^n - 3)/4, {n, 0, 50}] (* or *)
LinearRecurrence[{1, 1, -1}, {0, 0, 3, 3}, 50] (* G. C. Greubel, Jul 16 2016 *)
With[{c=Range[0, 108, 3]}, Riffle[c, c]] (* Harvey P. Dale, Feb 03 2021 *)

Prog

(Magma) [3*n/2-3/4+3*(-1)^n/4: n in [0..70]]; // Vincenzo Librandi, Sep 16 2013

Crossrefs

Cf. A008585, A110654.

Sequence in context: A227128 A061795 A110261 * A290966 A049318 A325861

Adjacent sequences: A168234 A168235 A168236 * A168238 A168239 A168240

Keyword

nonn,easy,changed

Author

Vincenzo Librandi, Nov 21 2009

Extensions

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

a(0)=0 added by N. J. A. Sloane, Feb 02 2021 at the suggestion of Allan C. Wechsler

Status

approved