login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A291703 Number of connected dominating sets in the complete tripartite graph K_{n,n,n}. 2
7, 54, 490, 4050, 32674, 261954, 2096770, 16776450, 134216194, 1073738754, 8589928450, 68719464450, 549755789314, 4398046461954, 35184371990530, 281474976514050, 2251799813292034, 18014398508695554, 144115188074283010, 1152921504603701250 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For n > 1, the only dominating sets that are not connected are the 3 sets consisting of all vertices from a single partition. For n > 1, the only connected sets that are not dominating are the 3n sets consisting of a single vertex. - Andrew Howroyd, Aug 30 2017

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Complete Tripartite Graph

Eric Weisstein's World of Mathematics, Connected Dominating Set

Index entries for linear recurrences with constant coefficients, signature (11,-26,16).

FORMULA

a(n) = A291537(n) - 3 = A290756(n) - 3*n for n > 1. - Andrew Howroyd, Aug 30 2017

From Colin Barker, Sep 01 2017: (Start)

G.f.: x*(7 - 23*x + 78*x^2 - 48*x^3) / ((1 - x)*(1 - 2*x)*(1 - 8*x)).

a(n) = 2 - 3*2^n + 8^n for n > 1.

a(n) = 11*a(n-1) - 26*a(n-2) + 16*a(n-3) for n > 4.

(End)

a(n) = A302942(n) for n > 1. - Eric W. Weisstein, Apr 16 2018

MATHEMATICA

a[1] = 7; a[n_] := 2 - 3*2^n + 8^n; Array[a, 20] (* Jean-Fran├žois Alcover, Oct 08 2017 *)

(* Start from Eric W. Weisstein, Oct 12 2017 *)

Table[Piecewise[{{7, n == 1}}, 2 - 3 2^n + 8^n], {n, 20}]

Table[Piecewise[{{7, n == 1}}, 2 (2^(n - 1) + 1) (2^n - 1)^2], {n, 20}]

Join[{7}, LinearRecurrence[{11, -26, 16}, {54, 490, 4050}, 20]]

CoefficientList[Series[(-7 + 23 x - 78 x^2 + 48 x^3)/(-1 + 11 x - 26 x^2 + 16 x^3), {x, 0, 20}], x]

(* End *)

PROG

(PARI) a(n) = if(n < 2, [7][n], 8^n - 3*2^n + 2); \\ Andrew Howroyd, Aug 30 2017

(PARI) Vec(x*(7 - 23*x + 78*x^2 - 48*x^3) / ((1 - x)*(1 - 2*x)*(1 - 8*x)) + O(x^30)) \\ Colin Barker, Sep 01 2017

CROSSREFS

Cf. A290756, A291537.

Cf. A302942.

Sequence in context: A243670 A152108 A093742 * A014509 A228415 A084065

Adjacent sequences:  A291700 A291701 A291702 * A291704 A291705 A291706

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Aug 30 2017

EXTENSIONS

a(8)-a(20) from Andrew Howroyd, Aug 30 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 4 05:42 EST 2021. Contains 341779 sequences. (Running on oeis4.)