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%I #29 Apr 26 2023 12:57:30
%S 6,33,188,985,4990,24645,119712,574225,2727218,12847821,60115060,
%T 279652793,1294441894,5965567125,27387631368,125308264225,
%U 571591760602,2600204421405,11799376912220,53424388364873,241398575303374,1088727972172389,4901842528232304,22034981672761649
%N Number of connected induced (non-null) subgraphs of the web graph with 3n nodes.
%H Andrew Howroyd, <a href="/A286187/b286187.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</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_08">Index entries for linear recurrences with constant coefficients</a>, signature (12, -50, 80, -17, -76, 52, 16, -16).
%F Empirical g.f.: x*(6 - 39*x + 92*x^2 - 101*x^3 + 32*x^4 - 8*x^5 + 64*x^6 - 48*x^7) / ((1 - x)^2*(1 - 5*x + 2*x^2 + 4*x^3)^2). - _Colin Barker_, May 21 2017
%t {6, 33} ~Join~ Table[g = GraphData[{"Web", n}]; -1 + ParallelSum[Boole@ ConnectedGraphQ@ Subgraph[g, s], {s, Subsets@ Range[3 n]}], {n, 3, 6}]
%t LinearRecurrence[{12, -50, 80, -17, -76, 52, 16, -16},{6, 33, 188, 985, 4990, 24645, 119712, 574225},200] (* _Ray Chandler_, Apr 26 2023 *)
%Y Cf. A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286185 (Möbius ladder), A286186 (friendship), A286188 (gear), A286189 (rook), A285765 (queen).
%K nonn
%O 1,1
%A _Giovanni Resta_, May 04 2017
%E a(12)-a(24) from _Andrew Howroyd_, May 20 2017
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