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A286188 Number of connected induced (non-null) subgraphs of the gear graph with 2n+1 nodes. 16
6, 26, 76, 218, 664, 2174, 7452, 26130, 92512, 328774, 1170052, 4166106, 14836488, 52839374, 188188396, 670240802, 2387095600, 8501764310, 30279479508, 107841961962, 384084839128, 1367938434910, 4871984975932, 17351831789874, 61799465313024 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Gear Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
FORMULA
a(n) = 6*a(n-1) - 10*a(n-2) + 4*a(n-3) + 3*a(n-4) - 2*a(n-5), for n>5.
a(n) = A206776(n) + 4*n^2 - 2*n + 1. - Eric W. Weisstein, May 08 2017
G.f.: 2*x*(3 - 5*x - 10*x^2 - x^3 - 3*x^4) / ((1 - x)^3*(1 - 3*x - 2*x^2)). - Colin Barker, May 31 2017
MATHEMATICA
a[n_] := Block[{g = Graph@ Flatten[{Table[i <-> 2 n + 1, {i, 2, 2 n, 2}], Table[i <-> Mod[i, 2 n] + 1, {i, 2 n}]}]}, -1 + ParallelSum[ Boole@ ConnectedGraphQ@ Subgraph[g, s], {s, Subsets@ Range[2 n + 1]}]]; Array[a, 8]
CROSSREFS
Cf. A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286185 (Möbius ladder), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen).
Sequence in context: A241452 A175898 A255870 * A335648 A094162 A229572
KEYWORD
nonn
AUTHOR
Giovanni Resta, May 04 2017
EXTENSIONS
a(16)-a(25) from Andrew Howroyd, May 20 2017
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)