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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. 1
 13, 23, 41, 77, 141, 259, 477, 877, 1613, 2967, 5457, 10037, 18461, 33955, 62453, 114869, 211277, 388599, 714745, 1314621, 2417965, 4447331, 8179917, 15045213, 27672461, 50897591, 93615265, 172185317, 316698173, 582498755 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. a(n) = Sum_{k>=1} A213654(n,k). REFERENCES S. Alikhani and Y. H. Peng, Dominating sets and domination polynomials of certain graphs, II, Opuscula Math., 30, No. 1, 2010, 37-51. LINKS Table of n, a(n) for n=1..30. S. Alikhani and Y. H. Peng, Introduction to domination polynomial of a graph, arXiv:0905.2251. Index entries for linear recurrences with constant coefficients, signature (1,1,1). FORMULA a(n) = a(n-1) + a(n-2) + a(n-3) for n >= 4; a(1)=13, a(2)=23, a(3)=41. G.f.: -x*(13+10*x+5*x^2)/(-1+x+x^2+x^3). - R. J. Mathar, Jul 22 2022 EXAMPLE 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}. MAPLE 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); MATHEMATICA LinearRecurrence[{1, 1, 1}, {13, 23, 41}, 30] (* Jean-François Alcover, Dec 02 2017 *) CROSSREFS Cf. A213654. Sequence in context: A339867 A135283 A225519 * A119488 A165350 A236418 Adjacent sequences: A213652 A213653 A213654 * A213656 A213657 A213658 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 18 2012 STATUS approved

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Last modified September 9 07:24 EDT 2024. Contains 375762 sequences. (Running on oeis4.)