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A178674 a(n) = 3^n + 3.

%I A178674 #41 Apr 02 2025 20:29:23
%S A178674 4,6,12,30,84,246,732,2190,6564,19686,59052,177150,531444,1594326,
%T A178674 4782972,14348910,43046724,129140166,387420492,1162261470,3486784404,
%U A178674 10460353206,31381059612,94143178830,282429536484,847288609446,2541865828332,7625597484990,22876792454964
%N A178674 a(n) = 3^n + 3.
%C A178674 a(n) is the deficiency of 3^n * 5. - _Patrick J. McNab_, May 27 2017
%H A178674 Vincenzo Librandi, <a href="/A178674/b178674.txt">Table of n, a(n) for n = 0..1000</a>
%H A178674 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A178674 a(n) = 3*(a(n-1) - 2), a(0)=4.
%F A178674 From _R. J. Mathar_, Jan 05 2011: (Start)
%F A178674 G.f.: (4-10*x)/((1-3*x)*(1-x)).
%F A178674 a(n) = 2*A115098(n). (End)
%F A178674 a(n) = 4*a(n-1) - 3*a(n-2) for n > 1. - _Vincenzo Librandi_, May 13 2014
%F A178674 E.g.f.: exp(x)*(exp(2*x) + 3). - _Elmo R. Oliveira_, Apr 02 2025
%t A178674 Table[3^n+3, {n, 0, 40}] (* or *) CoefficientList[Series[(4-10x)/((1-x) (1-3x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, May 13 2014 *)
%o A178674 (Magma)[3^n+3: n in [0..35]];
%o A178674 (PARI) a(n)=3^n+3 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A178674 (Sage) [3^n+3 for n in range(40)] # _G. C. Greubel_, Jan 27 2019
%o A178674 (GAP) List([0..40], n -> 3^n+3); # _G. C. Greubel_, Jan 27 2019
%Y A178674 Cf. A034472, A115098, A168607, A168609, A168610.
%K A178674 nonn,easy
%O A178674 0,1
%A A178674 _Vincenzo Librandi_, Dec 25 2010