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A213655 Number of dominating subsets of the theta-graph TH(2,2,n) (n>=1). A tribonacci sequence with initial values 13, 23, and 41.

%I A213655 #17 Jan 14 2024 20:33:42
%S A213655 13,23,41,77,141,259,477,877,1613,2967,5457,10037,18461,33955,62453,
%T A213655 114869,211277,388599,714745,1314621,2417965,4447331,8179917,15045213,
%U A213655 27672461,50897591,93615265,172185317,316698173,582498755
%N A213655 Number of dominating subsets of the theta-graph TH(2,2,n) (n>=1). A tribonacci sequence with initial values 13, 23, and 41.
%C A213655 A theta-graph is a graph consisting of two vertices of degree three, connected by three paths of one or more edges each. In the theta-graph TH(2,2,n) the three paths have 2, 2, and n edges, respectively.
%C A213655 a(n) = Sum_{k>=1} A213654(n,k).
%D A213655 S. Alikhani and Y. H. Peng, Dominating sets and domination polynomials of certain graphs, II, Opuscula Math., 30, No. 1, 2010, 37-51.
%H A213655 S. Alikhani and Y. H. Peng, <a href="http://arxiv.org/abs/0905.2251"> Introduction to domination polynomial of a graph</a>, arXiv:0905.2251.
%H A213655 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F A213655 a(n) = a(n-1) + a(n-2) + a(n-3) for n >= 4; a(1)=13, a(2)=23, a(3)=41.
%F A213655 G.f.: -x*(13+10*x+5*x^2)/(-1+x+x^2+x^3). - _R. J. Mathar_, Jul 22 2022
%e A213655 a(1)=13. TH(2,2,1) is the graph obtained from the cycle ABCD by joining vertices A and C. All 2^4 - 1 = 15 nonempty subsets of {A,B,C,D} are dominating with the exception of {B} and {D}.
%p A213655 a := proc (n) if n = 1 then 13 elif n = 2 then 23 elif n = 3 then 41 else a(n-1)+a(n-2)+a(n-3) end if end proc: seq(a(n), n = 1 .. 30);
%t A213655 LinearRecurrence[{1, 1, 1}, {13, 23, 41}, 30] (* _Jean-François Alcover_, Dec 02 2017 *)
%Y A213655 Cf. A213654.
%K A213655 nonn,easy
%O A213655 1,1
%A A213655 _Emeric Deutsch_, Jun 18 2012