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%I #20 Jan 14 2024 09:00:03
%S 2,3,6,15,42,123,366,1095,3282,9843,29526,88575,265722,797163,2391486,
%T 7174455,21523362,64570083,193710246,581130735,1743392202,5230176603,
%U 15690529806,47071589415,141214768242,423644304723,1270932914166
%N a(0) = 2, a(n) = 3*a(n-1) - 3.
%C Also the domination number of the (n+2)-Dorogovtsev-Goltsev-Mendes graph, where the convention DGM(0) = P_2 is used. - _Eric W. Weisstein_, Jan 14 2024
%H Vincenzo Librandi, <a href="/A115098/b115098.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Dorogovtsev-Goltsev-MendesGraph.html">Dorogovtsev-Goltsev-Mendes Graph</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F a(n) = (3^n + 3)/2.
%F a(n) = A067771(n-1), n > 0. - _R. J. Mathar_, Aug 11 2008
%F G.f.: (2-5*x)/((1-x)*(1-3*x)). - _Vincenzo Librandi_, Sep 13 2014
%e a(4) = (3^4 + 3)/2 = 84/2 = 42 = 3*a(3) - 3 = 3*15 - 3.
%p seq((3^i+3)/2,i=0..30);
%t CoefficientList[Series[(2 - 5 x)/((1 - x) (1 - 3 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 13 2014 *)
%t NestList[3 # - 3 &, 2, 30] (* _Harvey P. Dale_, Feb 05 2021 *)
%t Table[(3^n + 3)/2, {n, 0, 20}] (* _Eric W. Weisstein_, Jan 14 2024 *)
%t (3^Range[0, 20] + 3)/2 (* _Eric W. Weisstein_, Jan 14 2024 *)
%t LinearRecurrence[{4, -3}, {2, 3}, 20] (* _Eric W. Weisstein_, Jan 14 2024 *)
%o (Magma) [(3^n+3)/2: n in [0..30]]; // _Vincenzo Librandi_, Sep 13 2014
%o (PARI) a(n)=(3^n+3)/2 \\ _Charles R Greathouse IV_, Sep 13 2014
%Y Cf. A067771.
%K easy,nonn
%O 0,1
%A _Miklos Kristof_, Mar 02 2006
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