OFFSET
1,1
COMMENTS
Cases n=1 and n=2 correspond to degenerate prism graphs, but they fit the same (conjectured) linear recurrence as the other terms.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Prism Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
FORMULA
a(n) = 6*a(n-1) - 11*a(n-2) + 4*a(n-3) + 5*a(n-4) - 2*a(n-5) - a(n-6), for n > 6 (conjectured).
G.f.: x*(3 - 5*x + 6*x^2 - 8*x^3 - 5*x^4 - 3*x^5) / ((1 - x)^2*(1 - 2*x - x^2)^2) (conjectured). - Colin Barker, May 31 2017
MATHEMATICA
a[n_] := Block[{g = Graph@ Flatten@ Table[{i <-> Mod[i, n] + 1, n+i <-> Mod[i, n] + n+1, i <-> i+n}, {i, n}]}, -1 + ParallelSum[ Boole@ ConnectedGraphQ@ Subgraph[g, s], {s, Subsets@Range[2 n]}]]; Array[a, 8]
CROSSREFS
KEYWORD
nonn
AUTHOR
Giovanni Resta, May 04 2017
EXTENSIONS
Terms a(18) and beyond from Andrew Howroyd, Aug 15 2017
STATUS
approved