A165351 Numerator of 3*n/2.

0, 3, 3, 9, 6, 15, 9, 21, 12, 27, 15, 33, 18, 39, 21, 45, 24, 51, 27, 57, 30, 63, 33, 69, 36, 75, 39, 81, 42, 87, 45, 93, 48, 99, 51, 105, 54, 111, 57, 117, 60, 123, 63, 129, 66, 135, 69, 141, 72, 147, 75, 153, 78, 159, 81, 165, 84, 171, 87, 177, 90, 183, 93, 189, 96, 195

Offset

0,2

Comments

First trisection of A026741. The other trisections are A165355 and A165367.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Formula

a(n) = A026741(3*n) = 3*A026741(n).

a(2n) = A008585(n).

a(2n+1) = A016945(n).

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

a(n) = numerator(3n/2). - Wesley Ivan Hurt, Oct 11 2013

a(n) = 3*n / (1 + ((n+1) mod 2)). - Wesley Ivan Hurt, Feb 25 2014

From G. C. Greubel, Jul 31 2022: (Start)

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

E.g.f.: (3*x/2)*( 2*cosh(x) + sinh(x) ). (End)

Maple

A165351:=n->numer(3*n/2); seq(A165351(k), k=0..100); # Wesley Ivan Hurt, Oct 11 2013

Mathematica

Table[Numerator[3n/2], {n, 0, 100}] (* Wesley Ivan Hurt, Oct 11 2013 *)
CoefficientList[Series[3*x*(1+x+x^2)/(1-x^2)^2, {x, 0, 70}], x] (* Vincenzo Librandi, Mar 03 2014 *)
LinearRecurrence[{0, 2, 0, -1}, {0, 3, 3, 9}, 70] (* Harvey P. Dale, Jun 20 2021 *)

Prog

(Magma) [Numerator(3*n/2): n in [0..100]]; // Vincenzo Librandi, Mar 03 2014
(SageMath) [3*n*(3-(-1)^n)/4 for n in (0..100)] # G. C. Greubel, Jul 31 2022

Crossrefs

Cf. A000034 (denominator).

Cf. A008585, A016945, A026741, A098832, A165355, A165367.

Sequence in context: A247571 A292885 A227075 * A215665 A200494 A156164

Adjacent sequences: A165348 A165349 A165350 * A165352 A165353 A165354

Keyword

nonn,easy

Author

Paul Curtz, Sep 16 2009

Extensions

Edited and extended by R. J. Mathar, Sep 26 2009

New name from Wesley Ivan Hurt, Oct 13 2013

Status

approved