This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A115098 #24 Mar 13 2025 09:51:00
%S A115098 2,3,6,15,42,123,366,1095,3282,9843,29526,88575,265722,797163,2391486,
%T A115098 7174455,21523362,64570083,193710246,581130735,1743392202,5230176603,
%U A115098 15690529806,47071589415,141214768242,423644304723,1270932914166
%N A115098 a(0) = 2, a(n) = 3*a(n-1) - 3.
%C A115098 Also the domination and connected 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 and Mar 13 2025
%H A115098 Vincenzo Librandi, <a href="/A115098/b115098.txt">Table of n, a(n) for n = 0..1000</a>
%H A115098 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedDominationNumber.html">Connected Domination Number</a>.
%H A115098 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>.
%H A115098 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Dorogovtsev-Goltsev-MendesGraph.html">Dorogovtsev-Goltsev-Mendes Graph</a>.
%H A115098 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A115098 a(n) = (3^n + 3)/2.
%F A115098 a(n) = A067771(n-1), n > 0. - _R. J. Mathar_, Aug 11 2008
%F A115098 G.f.: (2-5*x)/((1-x)*(1-3*x)). - _Vincenzo Librandi_, Sep 13 2014
%e A115098 a(4) = (3^4 + 3)/2 = 84/2 = 42 = 3*a(3) - 3 = 3*15 - 3.
%p A115098 seq((3^i+3)/2,i=0..30);
%t A115098 CoefficientList[Series[(2 - 5 x)/((1 - x) (1 - 3 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 13 2014 *)
%t A115098 NestList[3 # - 3 &, 2, 30] (* _Harvey P. Dale_, Feb 05 2021 *)
%t A115098 Table[(3^n + 3)/2, {n, 0, 20}] (* _Eric W. Weisstein_, Jan 14 2024 *)
%t A115098 (3^Range[0, 20] + 3)/2 (* _Eric W. Weisstein_, Jan 14 2024 *)
%t A115098 LinearRecurrence[{4, -3}, {2, 3}, 20] (* _Eric W. Weisstein_, Jan 14 2024 *)
%o A115098 (Magma) [(3^n+3)/2: n in [0..30]]; // _Vincenzo Librandi_, Sep 13 2014
%o A115098 (PARI) a(n)=(3^n+3)/2 \\ _Charles R Greathouse IV_, Sep 13 2014
%Y A115098 Cf. A067771.
%K A115098 easy,nonn
%O A115098 0,1
%A A115098 _Miklos Kristof_, Mar 02 2006