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A127226 a(n) = 2*a(n-1) + 6*a(n-2) with a(0)=2, a(1)=2.

%I A127226 #29 Dec 30 2024 21:54:41
%S A127226 2,2,16,44,184,632,2368,8528,31264,113696,414976,1512128,5514112,
%T A127226 20100992,73286656,267179264,974078464,3551232512,12946935808,
%U A127226 47201266688,172084148224,627375896576,2287256682496,8338768744448,30401077583872,110834767634432,404076000772096
%N A127226 a(n) = 2*a(n-1) + 6*a(n-2) with a(0)=2, a(1)=2.
%H A127226 Andrew Howroyd, <a href="/A127226/b127226.txt">Table of n, a(n) for n = 0..500</a>
%H A127226 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,6).
%F A127226 G.f.: 2*(1 - x)/(1 - 2*x - 6*x^2).
%F A127226 E.g.f.: (exp((1+sqrt(7))*x) + exp((1-sqrt(7))*x));
%F A127226 a(n) = A083099(n) + 6*A083099(n-2).
%F A127226 G.f.: G(0), where G(k)= 1 + 1/(1 - x*(7*k-1)/(x*(7*k+6) - 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 03 2013
%F A127226 a(n) = 2*A083098(n). - _Andrew Howroyd_, Dec 30 2024
%t A127226 a[0]=2;a[1]=2;a[n_]:=2a[n-1]+6a[n-2];Table[a[n],{n,0,22}] (* _James C. McMahon_, Dec 30 2024 *)
%o A127226 (Sage) [lucas_number2(n,2,-6) for n in range(0, 23)] # _Zerinvary Lajos_, Apr 30 2009
%o A127226 (PARI) Vec(2*(1 - x)/(1 - 2*x - 6*x^2) + O(x^31)) \\ _Andrew Howroyd_, Dec 30 2024
%Y A127226 Cf. A083098, A083099.
%K A127226 easy,nonn
%O A127226 0,1
%A A127226 _Miklos Kristof_, Mar 26 2007
%E A127226 a(23) onwards from _Andrew Howroyd_, Dec 30 2024