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A287471
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Number of connected dominating sets in the n-crown graph.
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2
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13, 115, 666, 3234, 14379, 60981, 251968, 1026124, 4145241, 16670823, 66879606, 267944070, 1072693399, 4292739241, 17175150780, 68709515472, 274856935653, 1099467587835, 4397954236690, 17591993106730, 70368341524803, 281474137850205, 1125898162012536
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OFFSET
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3,1
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COMMENTS
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A connected dominating set in the crown graph requires a minimum two vertices on each side of the graph which cannot be two pairs of opposing vertices. - Andrew Howroyd, Jun 03 2017
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LINKS
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FORMULA
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G.f.: x^3*(13 - 28*x + 12*x^2) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)).
a(n) = 11*a(n-1) - 47*a(n-2) + 101*a(n-3) - 116*a(n-4) + 68*a(n-5) - 16*a(n-6) for n>8.
(End)
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PROG
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(PARI) Vec(x^3*(13 - 28*x + 12*x^2) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Jun 03 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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