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URL: https://oeis.org/A165351

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A165351
Numerator of 3*n/2.
7
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.
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).
Sequence in context: A247571 A292885 A227075 * A215665 A200494 A156164
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