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 A286186 Number of connected induced (non-null) subgraphs of the friendship graph with 2n+1 nodes. 15
 7, 22, 73, 268, 1039, 4114, 16405, 65560, 262171, 1048606, 4194337, 16777252, 67108903, 268435498, 1073741869, 4294967344, 17179869235, 68719476790, 274877907001, 1099511627836, 4398046511167, 17592186044482, 70368744177733, 281474976710728, 1125899906842699 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Wikipedia, Friendship graph Eric Weisstein's World of Mathematics, Dutch Windmill Graph Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph Index entries for linear recurrences with constant coefficients, signature (6,-9,4). FORMULA a(n) = 4^n + 3*n. From Colin Barker, May 21 2017: (Start) G.f.: x*(7 - 20*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)). a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3) for n>3. (End) MATHEMATICA Table[4^n + 3 n, {n, 30}] LinearRecurrence[{6, -9, 4}, {7, 22, 73}, 40] (* Harvey P. Dale, May 25 2019 *) PROG (PARI) Vec(x*(7 - 20*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)) + O(x^30)) \\ Colin Barker, May 21 2017 CROSSREFS Cf. A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286185 (Möbius ladder), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen). Sequence in context: A101289 A085287 A278767 * A282035 A302273 A151822 Adjacent sequences:  A286183 A286184 A286185 * A286187 A286188 A286189 KEYWORD nonn,easy AUTHOR Giovanni Resta, May 04 2017 STATUS approved

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Last modified August 26 03:18 EDT 2019. Contains 326324 sequences. (Running on oeis4.)