VOOZH about

URL: https://oeis.org/A213661

⇱ A213661 - OEIS

login
A213661
Number of dominating subsets of the wheel graph W_n.
2
4, 3, 7, 15, 27, 53, 103, 199, 387, 753, 1467, 2863, 5595, 10949, 21455, 42095, 82691, 162625, 320179, 631031, 1244907, 2458261, 4858487, 9610231, 19024131, 37687153, 74710123, 148198623, 294150331, 584167941, 1160734623, 2307488351, 4589261827
OFFSET
1,1
COMMENTS
a(n) = Sum_{k=1..n} A212635(n,k).
Extended to a(1)-a(3) using the formula/recurrence.
LINKS
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.
Eric Weisstein's World of Mathematics, Dominating Set
Eric Weisstein's World of Mathematics, Wheel Graph
FORMULA
a(n) = a(n-1) + a(n-2) + a(n-3) + 2^(n-4) for n >= 4.
G.f.: x*(4 - 9*x + 2*x^2 + x^3)/(1 - 3*x + x^2 + x^3 + 2*x^4).
a(n) = 2^(n-1) -A000073(n+2)+4*A000073(n+1) -A000073(n). - R. J. Mathar, Jun 29 2012
a(n) = 3*a(n-1) - a(n-2) - a(n-3) - 2*a(n-4). - Eric W. Weisstein, Apr 17 2018
EXAMPLE
a(4)=15 because all nonempty subsets of the wheel W_4 are dominating (2^4 - 1 = 15).
MAPLE
a[4] := 15: a[5] := 27: a[6] := 53: for n from 7 to 42 do a[n] := a[n-1]+a[n-2]+a[n-3]+2^(n-4) end do: seq(a[n], n = 4 .. 40);
MATHEMATICA
LinearRecurrence[{3, -1, -1, -2}, {4, 3, 7, 15}, 40] (* Eric W. Weisstein, Mar 31 2017 *)
Table[2^(n - 1) + RootSum[-1 - # - #^2 + #^3 &, #^n (-1 - # + #1^2) &], {n, 20}] (* Eric W. Weisstein, Apr 17 2018 *)
CoefficientList[Series[(4 - 9 x + 2 x^2 + x^3)/(1 - 3 x + x^2 + x^3 + 2 x^4), {x, 0, 20}], x] (* Eric W. Weisstein, Apr 17 2018 *)
CROSSREFS
Cf. A212635.
Sequence in context: A245300 A228949 A048227 * A176083 A092193 A277117
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 29 2012
EXTENSIONS
a(1)-a(3) prepended by Eric W. Weisstein, Apr 17 2018
STATUS
approved