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A168648 a(n) = (10*2^n + 2*(-1)^n)/3 for n > 0; a(0) = 1.

%I A168648 #18 Sep 08 2022 08:45:49
%S A168648 1,6,14,26,54,106,214,426,854,1706,3414,6826,13654,27306,54614,109226,
%T A168648 218454,436906,873814,1747626,3495254,6990506,13981014,27962026,
%U A168648 55924054,111848106,223696214,447392426,894784854,1789569706,3579139414
%N A168648 a(n) = (10*2^n + 2*(-1)^n)/3 for n > 0; a(0) = 1.
%H A168648 Vincenzo Librandi, <a href="/A168648/b168648.txt">Table of n, a(n) for n = 0..200</a>
%H A168648 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).
%F A168648 a(n) = A084214(n+2) for n > 0.
%F A168648 a(n) = a(n-1) + 2*a(n-2) for n > 2; a(0) = 1, a(1) = 6, a(2) = 14.
%F A168648 G.f.: (1+2*x)*(1+3*x)/((1+x)*(1-2*x)).
%F A168648 E.g.f.: (1/3)*(10*exp(2*x) - 9 + 2*exp(-x)). - _G. C. Greubel_, Jul 28 2016
%t A168648 {1}~Join~Table[(10*2^n + 2*(-1)^n)/3, {n,40}] (* or *)
%t A168648 {1}~Join~LinearRecurrence[{1,2}, {6,14}, 40] (* _G. C. Greubel_, Jul 28 2016 *)
%o A168648 (Magma) [1] cat [ (10*2^n+2*(-1)^n)/3: n in [1..30] ];
%o A168648 (PARI) a(n) = if(n, (10<<n + 2*(-1)^n)/3, 1) \\ _Charles R Greathouse IV_, Jul 29 2016
%o A168648 (Sage) [1]+[(10*2^n +2*(-1)^n)/3 for n in (1..40)] # _G. C. Greubel_, Feb 05 2021
%Y A168648 Cf. A084214 ((5*2^n -3*0^n +4*(-1)^n)/6).
%K A168648 nonn,easy
%O A168648 0,2
%A A168648 _Klaus Brockhaus_, Dec 01 2009