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A059525 Number of nonzero n X n binary arrays with all 1's connected. 17

%I

%S 0,1,13,218,11506,2301877,1732082741,4872949974666,51016818604894742,

%T 1980555831431088025753,284374318545830329487309785,

%U 150730745416633777472365437495914,294516896499779486414143877573183893666,2119097214294718323017954923662829194285541981

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

%C Old name was: "Number of n X n checkerboards in which the set of red squares is edge connected".

%C 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

%H Andrew Howroyd, <a href="/A059525/b059525.txt">Table of n, a(n) for n = 0..16</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/InducedSubgraph.html">Induced Subgraph</a>

%t Table[Count[Subgraph[GridGraph[{n, n}], #] & /@ Subsets[Range[n^2], {1, Infinity}], _?ConnectedGraphQ], {n, 4}] (* _Eric W. Weisstein_, May 01 2017 *)

%Y Main diagonal of A287151.

%Y 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).

%K nonn,hard

%O 0,3

%A _David Radcliffe_, Jan 21 2001

%E One more term from _John W. Layman_, Jan 25 2001

%E More terms from _R. H. Hardin_, Feb 28 2002

%E Clearer name from _R. H. Hardin_, Jul 06 2009

%E a(8)-a(9) from _Giovanni Resta_, May 03 2017

%E a(10)-a(13) from _Andrew Howroyd_, May 20 2017

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Last modified October 16 18:03 EDT 2019. Contains 328102 sequences. (Running on oeis4.)