%I #19 Aug 26 2024 19:07:25
%S 0,6,12,30,60,126,252,510,1020,2046,4092,8190,16380,32766,65532,
%T 131070,262140,524286,1048572,2097150,4194300,8388606,16777212,
%U 33554430,67108860,134217726,268435452,536870910
%N a(n) = 2*a(n-1) if n odd else 2*a(n-1) + 6.
%H Vincenzo Librandi, <a href="/A014131/b014131.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -2).
%F a(n) = 3*A026644(n), n > 0. [moved from A020988 by _R. J. Mathar_, Oct 21 2008]
%F From _R. J. Mathar_, Oct 21 2008: (Start)
%F G.f.: 6x/((1-2x)(1-x)(1+x)).
%F a(n) = 2^(n+2) - 3 - (-1)^n. (End)
%t Table[2^(n+2)-3-(-1)^n,{n,0,40}] (* or *) CoefficientList[Series[6x/((1-2x)(1-x)(1+x)),{x,0,30}],x] (* _Vincenzo Librandi_, Apr 03 2012 *)
%t nxt[{n_,a_}]:={n+1,If[EvenQ[n],2a,2a+6]}; NestList[nxt,{1,0},30][[;;,2]] (* or *) LinearRecurrence[ {2,1,-2},{0,6,12},30] (* _Harvey P. Dale_, Aug 26 2024 *)
%o (Magma) [2^(n+2)-3-(-1)^n: n in [0..30]]; // _Vincenzo Librandi_, Apr 03 2012
%Y Cf. A000975.
%K nonn
%O 0,2
%A _N. J. A. Sloane_