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%I #19 Sep 08 2022 08:44:59
%S 2,3,6,11,21,40,77,149,290,567,1113,2192,4329,8569,16994,33755,67133,
%T 133656,266325,531053,1059522,2114863,4222961,8434976,16852241,
%U 33675825,67305282,134535539,268949685,537702952,1075088093,2149661957
%N a(n) = 2^n + Fibonacci(n+1).
%H G. C. Greubel, <a href="/A052956/b052956.txt">Table of n, a(n) for n = 0..1000</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1027">Encyclopedia of Combinatorial Structures 1027</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-2).
%F G.f.: (2 -3*x -x^2)/((1-2*x)*(1-x-x^2)).
%F a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3).
%F a(n) = 2^n + Sum_{alpha=RootOf(-1+z+z^2)} (1 + 2*alpha)*alpha^(-1-n)/5.
%p spec:= [S,{S=Union(Sequence(Union(Prod(Z,Z),Z)),Sequence(Union(Z,Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
%p with(combinat); seq(2^n + fibonacci(n+1), n=0..40); # _G. C. Greubel_, Oct 22 2019
%t LinearRecurrence[{3,-1,-2}, {2,3,6}, 40] (* or *) Table[Fibonacci[n+1] + 2^n, {n,0,40}] (* _G. C. Greubel_, Oct 22 2019 *)
%o (PARI) vector(41, n, fibonacci(n) + 2^(n-1)) \\ _G. C. Greubel_, Oct 22 2019
%o (Magma) [2^n + Fibonacci(n+1): n in [0..40]]; // _G. C. Greubel_, Oct 22 2019
%o (Sage) [2^n + fibonacci(n+1) for n in (0..40)] # _G. C. Greubel_, Oct 22 2019
%o (GAP) List([0..40], n-> 2^n + Fibonacci(n+1) ); # _G. C. Greubel_, Oct 22 2019
%Y Cf. A000045, A000079.
%K easy,nonn
%O 0,1
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E More terms from _James A. Sellers_, Jun 05 2000
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