OFFSET
0,3
COMMENTS
Old name was: "Number of n X n checkerboards in which the set of red squares is edge connected".
Also the number of connected induced (non-null) subgraphs of the n X n grid graph P_n x P_n. - Eric W. Weisstein, May 01 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..16
Stijn Cambie, Jan Goedgebeur, and Jorik Jooken, The maximum number of connected sets in regular graphs, arXiv:2311.00075 [math.CO], 2023.
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Induced Subgraph
MATHEMATICA
Table[Count[Subgraph[GridGraph[{n, n}], #] & /@ Subsets[Range[n^2], {1, Infinity}], _?ConnectedGraphQ], {n, 4}] (* Eric W. Weisstein, May 01 2017 *)
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
David Radcliffe, Jan 21 2001
EXTENSIONS
One more term from John W. Layman, Jan 25 2001
More terms from R. H. Hardin, Feb 28 2002
Clearer name from R. H. Hardin, Jul 06 2009
a(8)-a(9) from Giovanni Resta, May 03 2017
a(10)-a(13) from Andrew Howroyd, May 20 2017
STATUS
approved