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 A286183 Number of connected induced (non-null) subgraphs of the antiprism graph with 2n nodes. 15
 3, 15, 60, 207, 663, 2038, 6107, 17983, 52272, 150407, 429223, 1216490, 3427635, 9609327, 26821668, 74576703, 206650167, 570877918, 1572754187, 4322192287, 11851474968, 32430381815, 88576465735, 241511251922, 657457204323, 1787147867343, 4851349002252 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 Eric Weisstein's World of Mathematics, Antiprism Graph Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph FORMULA a(n) = 8*a(n-1) - 24*a(n-2) + 34*a(n-3) - 24*a(n-4) + 8*a(n-5) - a(n-6), for n > 6 (conjectured). a(n) = A005248(n) - 2*n + 2*n*A001906(n) (conjectured). - Eric W. Weisstein, May 08 2017 G.f.: x*(3 - 9*x + 12*x^2 - 15*x^3 + 9*x^4 - 2*x^5) / ((1 - x)^2*(1 - 3*x + x^2)^2) (conjectured). - Colin Barker, May 30 2017 MATHEMATICA a[n_] := Block[{g = Graph@ Flatten@ Table[{i <-> Mod[i, n]+1, n+i <-> Mod[i, n] + n+1, i <-> n + Mod[i, n] + 1, i <-> n + Mod[i-1, n] + 1}, {i, n}]}, -1 + ParallelSum[ Boole@ ConnectedGraphQ@ Subgraph[g, s], {s, Subsets@ Range[2 n]}]]; Array[a, 8] CROSSREFS Cf. A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286184 (helm), A286185 (Möbius ladder), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen). Sequence in context: A128237 A176311 A036750 * A058748 A049314 A295505 Adjacent sequences:  A286180 A286181 A286182 * A286184 A286185 A286186 KEYWORD nonn AUTHOR Giovanni Resta, May 04 2017 EXTENSIONS a(17)-a(27) from Andrew Howroyd, May 20 2017 STATUS approved

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Last modified June 29 17:41 EDT 2022. Contains 354913 sequences. (Running on oeis4.)