OFFSET
3,1
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 [math.CO], 2009.
T. Kotek, J. Preen, F. Simon, P. Tittmann, and M. Trinks, Recurrence relations and splitting formulas for the domination polynomial, arXiv:1206.5926 [math.CO], 2012.
Index entries for linear recurrences with constant coefficients, signature (1,1,1).
FORMULA
a(n) = Sum_{k=1..n+1} A213664(n,k).
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 30 2012
STATUS
approved