A289255 a(n) = 4^n - 2*n - 1.

1, 11, 57, 247, 1013, 4083, 16369, 65519, 262125, 1048555, 4194281, 16777191, 67108837, 268435427, 1073741793, 4294967263, 17179869149, 68719476699, 274877906905, 1099511627735, 4398046511061, 17592186044371, 70368744177617, 281474976710607, 1125899906842573

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)).

Mathematica

Table[4^n - 2 n - 1, {n, 20}]
LinearRecurrence[{6, -9, 4}, {1, 11, 57}, 20]
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

Sequence in context: A101094 A187693 A200529 * A275795 A014470 A285448

Adjacent sequences: A289252 A289253 A289254 * A289256 A289257 A289258

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 29 2017

Status

approved