

A059525


Number of nonzero n X n binary arrays with all 1's connected.


20



0, 1, 13, 218, 11506, 2301877, 1732082741, 4872949974666, 51016818604894742, 1980555831431088025753, 284374318545830329487309785, 150730745416633777472365437495914, 294516896499779486414143877573183893666, 2119097214294718323017954923662829194285541981
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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 (nonnull) 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
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

Main diagonal of A287151.
Cf. A059021, A020873 (wheel), A059020 (ladder), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286185 (Möbius ladder), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen).
Sequence in context: A218475 A294982 A320627 * A086147 A329073 A015253
Adjacent sequences: A059522 A059523 A059524 * A059526 A059527 A059528


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



