A286188 Number of connected induced (non-null) subgraphs of the gear graph with 2n+1 nodes.

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

Offset

1,1

Links

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

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

Adjacent sequences: A286185 A286186 A286187 * A286189 A286190 A286191

Keyword

nonn

Author

Giovanni Resta, May 04 2017

Extensions

a(16)-a(25) from Andrew Howroyd, May 20 2017

Status

approved