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A165351 Numerator of 3*n/2.

%I A165351 #37 Aug 01 2022 08:12:04
%S A165351 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,
%T A165351 75,39,81,42,87,45,93,48,99,51,105,54,111,57,117,60,123,63,129,66,135,
%U A165351 69,141,72,147,75,153,78,159,81,165,84,171,87,177,90,183,93,189,96,195
%N A165351 Numerator of 3*n/2.
%C A165351 First trisection of A026741. The other trisections are A165355 and A165367.
%H A165351 Vincenzo Librandi, <a href="/A165351/b165351.txt">Table of n, a(n) for n = 0..1000</a>
%H A165351 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A165351 a(n) = A026741(3*n) = 3*A026741(n).
%F A165351 a(2n) = A008585(n).
%F A165351 a(2n+1) = A016945(n).
%F A165351 G.f.: 3*x*(1+x+x^2)/((1-x)^2 * (1+x)^2).
%F A165351 a(n) = numerator(3n/2). - _Wesley Ivan Hurt_, Oct 11 2013
%F A165351 a(n) = 3*n / (1 + ((n+1) mod 2)). - _Wesley Ivan Hurt_, Feb 25 2014
%F A165351 From _G. C. Greubel_, Jul 31 2022: (Start)
%F A165351 a(n) = 3*n*(3 - (-1)^n)/4.
%F A165351 E.g.f.: (3*x/2)*( 2*cosh(x) + sinh(x) ). (End)
%p A165351 A165351:=n->numer(3*n/2); seq(A165351(k), k=0..100); # _Wesley Ivan Hurt_, Oct 11 2013
%t A165351 Table[Numerator[3n/2], {n, 0, 100}] (* _Wesley Ivan Hurt_, Oct 11 2013 *)
%t A165351 CoefficientList[Series[3*x*(1+x+x^2)/(1-x^2)^2, {x, 0, 70}], x] (* _Vincenzo Librandi_, Mar 03 2014 *)
%t A165351 LinearRecurrence[{0,2,0,-1},{0,3,3,9},70] (* _Harvey P. Dale_, Jun 20 2021 *)
%o A165351 (Magma) [Numerator(3*n/2): n in [0..100]]; // _Vincenzo Librandi_, Mar 03 2014
%o A165351 (SageMath) [3*n*(3-(-1)^n)/4 for n in (0..100)] # _G. C. Greubel_, Jul 31 2022
%Y A165351 Cf. A000034 (denominator).
%Y A165351 Cf. A008585, A016945, A026741, A098832, A165355, A165367.
%K A165351 nonn,easy
%O A165351 0,2
%A A165351 _Paul Curtz_, Sep 16 2009
%E A165351 Edited and extended by _R. J. Mathar_, Sep 26 2009
%E A165351 New name from _Wesley Ivan Hurt_, Oct 13 2013