%I #18 Sep 27 2017 15:07:10
%S 2,20,68,304,1232,5168,21408,89088,370112,1538560,6394368,26577664,
%T 110464512,459127808,1908282368,7931445248,32965660672,137016012800,
%U 569483091968,2366956929024,9837842644992,40889273090048,169949115056128,706363785412608,2935877583634432,12202461910794240
%N Number of independent vertex sets and vertex covers in the n-web graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/VertexCover.html">Vertex Cover</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WebGraph.html">Web Graph</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,8,4).
%F G.f.: -2*x*(1 + 8*x + 6*x^2)/(-1 + 2*x + 8*x^2 + 4*x^3).
%F a(n) = 2*a(n-1) + 8*a(n-2) + 4*a(n-3).
%t Table[RootSum[-4 - 8 # - 2 #^2 + #^3 &, #^n &], {n, 20}]
%t LinearRecurrence[{2, 8, 4}, {2, 20, 68}, 20]
%t CoefficientList[Series[-2 (1 + 8 x + 6 x^2)/(-1 + 2 x + 8 x^2 + 4 x^3), {x, 0, 20}], x] (* _Eric W. Weisstein_, Sep 27 2017 *)
%o (PARI) Vec(-2*x*(1+8*x+6*x^2)/(-1+2*x+8*x^2+4*x^3) + O(x^30)) \\ _Michel Marcus_, Sep 27 2017
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, May 25 2017