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A213665 Number of dominating subsets of the graph G(n) obtained by joining a vertex with two consecutive vertices of the cycle graph C_n (n >=3). 2
13, 23, 43, 79, 145, 267, 491, 903, 1661, 3055, 5619, 10335, 19009, 34963, 64307, 118279, 217549, 400135, 735963, 1353647, 2489745, 4579355, 8422747, 15491847, 28493949, 52408543, 96394339, 177296831, 326099713, 599790883, 1103187427 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

a(n) = Sum(A213664(n,k), k=1..n+1).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 3..1000

S. Alikhani and Y. H. Peng, Introduction to domination polynomial of a graph, arXiv:0905.2251.

T. Kotek, J. Preen, F. Simon, P. Tittmann, and M. Trinks, Recurrence relations and splitting formulas for the domination polynomial, arXiv:1206.5926.

Index entries for linear recurrences with constant coefficients, signature (1,1,1).

FORMULA

a(3)=13, a(4)=23, a(5)=43, a(n)=a(n-1)+a(n-2)+a(n-3) for n>=6

G.f. x^3 * (13+10*x+7*x^2) / ( 1-x-x^2-x^3 ). - R. J. Mathar, Jul 03 2012

EXAMPLE

a(3)=13 because G(3) is the square abcd with the additional edge bd; all nonempty subsets of {a,b,c,d} are dominating, with the exception of {a} and {c}: 2^4 - 1 - 2 = 13.

MAPLE

a[3] := 13: a[4] := 23: a[5] := 43: for n from 6 to 42 do a[n] := a[n-1]+a[n-2]+a[n-3] end do: seq(a[n], n = 3 .. 42);

MATHEMATICA

CoefficientList[Series[(13+10*x+7*x^2)/(1-x-x^2-x^3), {x, 0, 100}], x] (* Vincenzo Librandi, Aug 03 2012 *)

LinearRecurrence[{1, 1, 1}, {13, 23, 43}, 40] (* Harvey P. Dale, Dec 11 2012 *)

CROSSREFS

Cf. A213664

Sequence in context: A240113 A256177 A320752 * A068712 A103166 A154863

Adjacent sequences:  A213662 A213663 A213664 * A213666 A213667 A213668

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jun 30 2012

STATUS

approved

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Last modified July 31 06:15 EDT 2021. Contains 346369 sequences. (Running on oeis4.)