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%I #9 Sep 08 2022 08:45:50
%S 3,-1,5,3,13,19,45,83,173,339,685,1363,2733,5459,10925,21843,43693,
%T 87379,174765,349523,699053,1398099,2796205,5592403,11184813,22369619,
%U 44739245,89478483,178956973,357913939,715827885,1431655763,2863311533
%N a(n) = (2*2^n+7*(-1)^n)/3.
%C a(n) = A155980(n+2).
%C a(n) = A135351(n+3)-A135351(n+2).
%C Second binomial transform of a signed version of A005032 preceded by 3.
%C Inverse binomial transform of A008776 preceded by 3.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).
%F a(n) = a(n-1)+2*a(n-2) for n > 1; a(0) = 3, a(1) = -1.
%F a(n) = 2^n-a(n-1) for n > 0; a(0) = 3.
%F G.f.: (3-4*x)/((1+x)*(1-2*x)).
%t Nest[Append[#,Last[#]+2#[[-2]]]&,{3,-1},40] (* _Harvey P. Dale_, Apr 07 2011 *)
%o (Magma) [ (2*2^n+7*(-1)^n)/3: n in [0..32] ];
%Y Cf. A155980 (First differences of A135351), A135351 ((2^n+3-7*(-1)^n+3*0^n)/6), A005032 (7*3^n), A008776 (2*3^n).
%K sign,easy
%O 0,1
%A _Klaus Brockhaus_, Dec 07 2009
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