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A287431 Number of connected dominating sets in the n-gear graph. 1
7, 21, 45, 129, 373, 1177, 3741, 12065, 38949, 125993, 407597, 1318961, 4268085, 13811769, 44695613, 144638017, 468058181, 1514668105, 4901568589, 15861809233, 51329892437, 166107021401, 537533612125, 1739495309409, 5629125066853, 18216231370857, 58948963008621 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

Eric Weisstein's World of Mathematics, Connected Dominating Set

Eric Weisstein's World of Mathematics, Gear Graph

Index entries for linear recurrences with constant coefficients, signature (4,-1,-6,4).

FORMULA

From Colin Barker, May 25 2017: (Start)

G.f.: x*(7 - 7*x - 32*x^2 + 12*x^3)/((1 - x)^2*(1 - 2*x - 4*x^2)).

a(n) = 1 + 4*n + (1-sqrt(5))^n + (1+sqrt(5))^n.

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

MATHEMATICA

LinearRecurrence[{4, -1, -6, 4}, {7, 21, 45, 129}, 20]

Table[2^n LucasL[n] + 4 n + 1, {n, 20}]

PROG

(PARI) Vec(x*(7 - 7*x - 32*x^2 + 12*x^3) / ((1 - x)^2*(1 - 2*x - 4*x^2)) + O(x^30)) \\ Colin Barker, May 25 2017

CROSSREFS

Sequence in context: A256051 A299254 A146411 * A127736 A212677 A146802

Adjacent sequences:  A287428 A287429 A287430 * A287432 A287433 A287434

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, May 25 2017

STATUS

approved

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Last modified May 17 23:07 EDT 2022. Contains 353779 sequences. (Running on oeis4.)