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Number of connected spanning subgraphs in the n X n grid graph.
4

%I #12 Jan 29 2023 17:21:36

%S 1,5,431,555195,10286937043,2692324030864335,9852929684161379901975,

%T 501079193080617800221189943995,

%U 352690403996687922642590703716802346343,3426297680513758764075706102615040790667832304415,458508006189588425325361635000918336126387961057365005349963

%N Number of connected spanning subgraphs in the n X n grid graph.

%C For n > 1, a(n) is the number of connected edge covers in the n X n grid graph.

%H Andrew Howroyd, <a href="/A359992/b359992.txt">Table of n, a(n) for n = 1..15</a>

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

%F a(n) = A053765(n) - A359989(n).

%e The a(2) = 5 connected spanning subgraphs are the following subgraphs and their rotations and reflections.

%e o---o o---o

%e | | |

%e o---o o---o

%Y Main diagonal of A359993.

%Y Cf. A007341, A053765, A080691, A286913, A359989.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Jan 28 2023