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A290270 Number of minimal dominating sets in the n-wheel graph. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified October 27 12:08 EDT 2021. Contains 348276 sequences. (Running on oeis4.)