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
KEYWORD
nonn
AUTHOR
Giovanni Resta, May 04 2017
EXTENSIONS
a(16)-a(25) from Andrew Howroyd, May 20 2017
STATUS
approved