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%I #12 Jun 03 2017 15:32:06
%S 13,115,666,3234,14379,60981,251968,1026124,4145241,16670823,66879606,
%T 267944070,1072693399,4292739241,17175150780,68709515472,274856935653,
%U 1099467587835,4397954236690,17591993106730,70368341524803,281474137850205,1125898162012536
%N Number of connected dominating sets in the n-crown graph.
%C 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
%H Andrew Howroyd, <a href="/A287471/b287471.txt">Table of n, a(n) for n = 3..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CrownGraph.html">Crown Graph</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-47,101,-116,68,-16).
%F a(n) = (2^n-n-1)^2 - n*(n-1)/2. - _Andrew Howroyd_, Jun 03 2017
%F From _Colin Barker_, Jun 03 2017: (Start)
%F G.f.: x^3*(13 - 28*x + 12*x^2) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)).
%F 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.
%F (End)
%o (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
%K nonn,easy
%O 3,1
%A _Eric W. Weisstein_, May 25 2017
%E Term a(13) and beyond from _Andrew Howroyd_, Jun 03 2017
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