A359992 Number of connected spanning subgraphs in the n X n grid graph.

1, 5, 431, 555195, 10286937043, 2692324030864335, 9852929684161379901975, 501079193080617800221189943995, 352690403996687922642590703716802346343, 3426297680513758764075706102615040790667832304415, 458508006189588425325361635000918336126387961057365005349963

Offset: 1

Author

Andrew Howroyd, Jan 28 2023

Keywords

• nonn

Comments

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

Examples

			The a(2) = 5 connected spanning subgraphs are the following subgraphs and their rotations and reflections.
   o---o   o---o
   |       |   |
   o---o   o---o
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..15
• Eric Weisstein's World of Mathematics, Grid Graph

Crossrefs

Main diagonal of A359993.

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

Formula

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