%I #27 Mar 13 2024 04:41:31
%S 1,4,9,25,63,183,513,1521,4455,13311,39609,118665,355023,1064583,
%T 3190833,9571041,28704375,86108751,258300009,774886905,2324581983,
%U 6973706583,20920883553,62762532561,188286889095,564860312991,1694578813209,5083735376745,15251199752943
%N "BIK" (reversible, indistinct, unlabeled) transform of 1,3,5,7...
%H Vincenzo Librandi, <a href="/A032127/b032127.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 For n>2, a(n) = (1/9)*((8-(-1)^n)*3^floor(n/2) + 2*3^n). - _Ralf Stephan_, May 11 2004
%F G.f.: -x*(3*x^4+5*x^3+6*x^2-x-1) / ((3*x-1)*(3*x^2-1)). - _Colin Barker_, Dec 15 2012
%t CoefficientList[Series[-(3 x^4 + 5 x^3 + 6 x^2 - x - 1)/((3 x - 1) (3 x^2 - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 19 2013 *)
%t LinearRecurrence[{3,3,-9},{1,4,9,25,63},30] (* _Harvey P. Dale_, Feb 20 2016 *)
%o (Magma) [1,4] cat [(1/9)*((8-(-1)^n)*3^Floor(n/2) + 2*3^n): n in [3..30]]; // _Vincenzo Librandi_, Oct 19 2013
%K nonn,easy
%O 1,2
%A _Christian G. Bower_
%E More terms from _Vincenzo Librandi_, Oct 19 2013