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%I #6 May 17 2017 22:42:57
%S 3,15,54,175,543,1642,4875,14271,41310,118487,337263,953810,2682579,
%T 7508655,20929158,58121407,160877055,443993146,1222110555,3355879647,
%U 9195143598,25144855655,68635721679,187035899810,508896450723,1382653280847,3751638404310
%N Number of connected dominating sets in the n-antiprism graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6,-1).
%F From _G. C. Greubel_, May 17 2017: (Start)
%F a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).
%F G.f.: (3*x - 3*x^2 - 3*x^3 - 2*x^4)/(1 - 6*x + 11*x^2 - 6*x^3 + x^4). (End)
%t Table[6 n ChebyshevU[n - 1, 3/2] + (1 - 2 n) LucasL[2 n], {n, 30}] (* _Eric W. Weisstein_, May 17 2017 *)
%t LinearRecurrence[{6, -11, 6, -1}, {3, 15, 54, 175}, 30] (* _Eric W. Weisstein_, May 17 2017 *)
%t Rest[CoefficientList[Series[(3*x - 3*x^2 - 3*x^3 - 2*x^4)/(1 - 6*x + 11*x^2 - 6*x^3 + x^4), {x,0,50}], x]] (* _G. C. Greubel_, May 17 2017 *)
%o (PARI) x='x+O('x^50); Vec((3*x - 3*x^2 - 3*x^3 - 2*x^4)/(1 - 6*x + 11*x^2 - 6*x^3 + x^4)) \\ _G. C. Greubel_, May 17 2017
%K nonn
%O 1,1
%A _Eric W. Weisstein_, May 17 2017
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