A115098 a(0) = 2, a(n) = 3*a(n-1) - 3.

2, 3, 6, 15, 42, 123, 366, 1095, 3282, 9843, 29526, 88575, 265722, 797163, 2391486, 7174455, 21523362, 64570083, 193710246, 581130735, 1743392202, 5230176603, 15690529806, 47071589415, 141214768242, 423644304723, 1270932914166

Offset: 0

Author

Miklos Kristof, Mar 02 2006

Keywords

• easy
• nonn

Comments

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

Examples

			a(4) = (3^4 + 3)/2 = 84/2 = 42 = 3*a(3) - 3 = 3*15 - 3.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Connected Domination Number.
• Eric Weisstein's World of Mathematics, Domination Number.
• Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.
• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A067771.

Programs

Magma

[(3^n+3)/2: n in [0..30]]; // Vincenzo Librandi, Sep 13 2014

Maple

seq((3^i+3)/2,i=0..30);

Mathematica

CoefficientList[Series[(2 - 5 x)/((1 - x) (1 - 3 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 13 2014 *)
NestList[3 # - 3 &, 2, 30] (* Harvey P. Dale, Feb 05 2021 *)
Table[(3^n + 3)/2, {n, 0, 20}] (* Eric W. Weisstein, Jan 14 2024 *)
(3^Range[0, 20] + 3)/2 (* Eric W. Weisstein, Jan 14 2024 *)
LinearRecurrence[{4, -3}, {2, 3}, 20] (* Eric W. Weisstein, Jan 14 2024 *)

PARI

a(n)=(3^n+3)/2 \\ Charles R Greathouse IV, Sep 13 2014

Formula

a(n) = (3^n + 3)/2.

a(n) = A067771(n-1), n > 0. - R. J. Mathar, Aug 11 2008

G.f.: (2-5*x)/((1-x)*(1-3*x)). - Vincenzo Librandi, Sep 13 2014