

A213655


Number of dominating subsets of the thetagraph 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 thetagraph is a graph consisting of two vertices of degree three, connected by three paths of one or more edges each. In the thetagraph TH(2,2,n) the three paths have 2, 2, and n edges, respectively.


REFERENCES

S. Alikhani and Y. H. Peng, Dominating sets and domination polynomials of certain graphs, II, Opuscula Math., 30, No. 1, 2010, 3751.


LINKS



FORMULA

a(n) = a(n1) + a(n2) + a(n3) 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(n1)+a(n2)+a(n3) end if end proc: seq(a(n), n = 1 .. 30);


MATHEMATICA



CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



