A290270 Number of minimal dominating sets in the n-wheel graph.

3, 4, 7, 6, 6, 15, 15, 22, 28, 45, 58, 79, 115, 159, 223, 307, 438, 609, 852, 1194, 1675, 2347, 3282, 4606, 6451, 9040, 12663, 17749, 24871, 34845, 48831, 68424, 95883, 134350, 188266, 263811, 369667, 518002, 725860, 1017129, 1425262, 1997179, 2798583

Offset

3,1

Comments

The n-wheel graph is well defined for n >= 4. If the sequence is extended to n=1 using A253413 then the initial terms are 1,2,3,4,... If the sequence is extended using the recurrence the initial terms are 7,1,3,4,... - Andrew Howroyd, Jul 27 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..1000

Eric Weisstein's World of Mathematics, Minimal Dominating Set

Eric Weisstein's World of Mathematics, Wheel Graph

Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, -1, -1, 1).

Formula

From Andrew Howroyd, Jul 27 2017: (Start)

a(n) = A253413(n-1) + 1 for n > 2.

a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-6) - 1 for n>8.

G.f.: x*(7 - 6*x - 5*x^2 + 2*x^5 + x^6) / ((1 - x^2 - x^3 -x^4 + x^6)*(1 - x)).

(End)

G.f.: x^3*(3+x-5*x^3-7*x^4+6*x^5+x^6)/((1-x^2-x^3-x^4+x^6)*(1-x)). - Vincenzo Librandi, Aug 04 2017

Mathematica

Table[1 + RootSum[1 - #1^2 - #1^3 - #1^4 + #1^6 &, #^(n - 1) &], {n, 3, 20}] (* Eric W. Weisstein, Aug 04 2017 *)
LinearRecurrence[{1, 1, 0, 0, -1, -1, 1}, {3, 4, 7, 6, 6, 15, 15}, 20] (* Eric W. Weisstein, Aug 04 2017 *)
CoefficientList[Series[(3 + x - 5 x^3 - 7 x^4 + 6 x^5 + x^6)/((1 - x^2 - x^3 - x^4 + x^6) (1-x)), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 04 2017 *)

Prog

(PARI)
Vec(((7-6*x-5*x^2+2*x^5+x^6)) / ((1-x^2-x^3-x^4+x^6)*(1-x)) + O(x^40)) \\ Andrew Howroyd, Jul 27 2017
(Magma) I:=[3, 4, 7, 6, 6, 15, 15, 22, 28]; [n le 9 select I[n] else Self(n-2)+Self(n-3)+Self(n-4)-Self(n-6)-1: n in [1..50]]; // Vincenzo Librandi, Aug 04 2017

Crossrefs

Cf. A253413.

Sequence in context: A284326 A117553 A331694 * A168275 A325968 A325818

Adjacent sequences: A290267 A290268 A290269 * A290271 A290272 A290273

Keyword

nonn

Author

Eric W. Weisstein, Jul 25 2017

Extensions

a(3) and a(16)-a(45) from Andrew Howroyd, Jul 27 2017

Status

approved