A286187 Number of connected induced (non-null) subgraphs of the web graph with 3n nodes.

6, 33, 188, 985, 4990, 24645, 119712, 574225, 2727218, 12847821, 60115060, 279652793, 1294441894, 5965567125, 27387631368, 125308264225, 571591760602, 2600204421405, 11799376912220, 53424388364873, 241398575303374, 1088727972172389, 4901842528232304, 22034981672761649

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph

Eric Weisstein's World of Mathematics, Web Graph

Index entries for linear recurrences with constant coefficients, signature (12, -50, 80, -17, -76, 52, 16, -16).

Formula

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

Mathematica

{6, 33} ~Join~ Table[g = GraphData[{"Web", n}]; -1 + ParallelSum[Boole@ ConnectedGraphQ@ Subgraph[g, s], {s, Subsets@ Range[3 n]}], {n, 3, 6}]
LinearRecurrence[{12, -50, 80, -17, -76, 52, 16, -16}, {6, 33, 188, 985, 4990, 24645, 119712, 574225}, 200] (* Ray Chandler, Apr 26 2023 *)

Crossrefs

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).

Sequence in context: A367850 A180035 A360717 * A260774 A218182 A093964

Adjacent sequences: A286184 A286185 A286186 * A286188 A286189 A286190

Keyword

nonn

Author

Giovanni Resta, May 04 2017

Extensions

a(12)-a(24) from Andrew Howroyd, May 20 2017

Status

approved