OFFSET
1,2
COMMENTS
Number of dominating sets in the n-cocktail party graph.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Cocktail Party Graph.
Eric Weisstein's World of Mathematics, Dominating Set.
Index entries for linear recurrences with constant coefficients, signature (6,-9,4).
FORMULA
a(n) = 4^n - 2*n - 1.
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).
G.f.: (-1 - 5*x)*x/((-1 + x)^2*(-1 + 4*x)).
From Elmo R. Oliveira, Apr 02 2025: (Start)
E.g.f.: exp(x)*(exp(3*x) - (2*x + 1)).
MATHEMATICA
Table[4^n - 2 n - 1, {n, 20}]
(* Alternative: *)
LinearRecurrence[{6, -9, 4}, {1, 11, 57}, 20]
(* Alternative: *)
CoefficientList[Series[(-1 - 5 x)/((-1 + x)^2 (-1 + 4 x)), {x, 0, 20}], x]
PROG
(PARI) Vec(x*(1 + 5*x) / ((1 - x)^2*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Jun 30 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 29 2017
STATUS
approved