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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
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Connected Dominating Set
Eric Weisstein's World of Mathematics, Gear Graph
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, May 25 2017
STATUS
approved