A032124 - OEIS

%I #28 Mar 13 2024 04:41:24

%S 2,5,12,33,90,261,756,2241,6642,19845,59292,177633,532170,1595781,

%T 4785156,14353281,43053282,129153285,387440172,1162300833,3486843450,

%U 10460471301,31381236756,94143533121,282430067922,847289672325,2541867422652,7625600673633

%N "BIK" (reversible, indistinct, unlabeled) transform of 2,2,2,2...

%H Vincenzo Librandi, <a href="/A032124/b032124.txt">Table of n, a(n) for n = 1..1000</a>

%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-9).

%F a(n) = (1/6)*((5-(-1)^n)*3^floor(n/2) + 2*3^n). - _Ralf Stephan_, May 11 2004

%F a(n) = 3*a(n-1)+3*a(n-2)-9*a(n-3). G.f.: -x*(9*x^2+x-2) / ((3*x-1)*(3*x^2-1)). - _Colin Barker_, Dec 15 2012

%t CoefficientList[Series[-(9 x^2 + x - 2)/((3 x - 1) (3 x^2 - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 19 2013 *)

%o (Magma) [(1/6)*((5-(-1)^n)*3^Floor(n/2) + 2*3^n): n in [1..30]]; // _Vincenzo Librandi_, Oct 19 2013

%K nonn,easy

%O 1,1

%A _Christian G. Bower_

%E More terms from _Vincenzo Librandi_, Oct 19 2013