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A286183
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Number of connected induced (non-null) subgraphs of the antiprism graph with 2n nodes.
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15
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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
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listen;
history;
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OFFSET
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1,1
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LINKS
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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
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FORMULA
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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) = LucasL[2*n] - 2*n + 2*n*Fibonacci[2*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
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MATHEMATICA
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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]
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Giovanni Resta, May 04 2017
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EXTENSIONS
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a(17)-a(27) from Andrew Howroyd, May 20 2017
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STATUS
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approved
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