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

Author

Paul Curtz, Sep 16 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000034 (denominator).

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

Programs

Magma

[Numerator(3*n/2): n in [0..100]]; // Vincenzo Librandi, Mar 03 2014

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 *)

SageMath

[3*n*(3-(-1)^n)/4 for n in (0..100)] # G. C. Greubel, Jul 31 2022

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)

Extensions

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

New name from Wesley Ivan Hurt, Oct 13 2013