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A288025
Array read by antidiagonals: T(m,n) = number of minimal edge covers in the grid graph P_m X P_n.
5
0, 1, 1, 1, 2, 1, 1, 6, 6, 1, 2, 17, 38, 17, 2, 2, 45, 190, 190, 45, 2, 3, 120, 1021, 1834, 1021, 120, 3, 4, 324, 5494, 19988, 19988, 5494, 324, 4, 5, 873, 29042, 208186, 419710, 208186, 29042, 873, 5, 7, 2349, 154772, 2177591, 8704085, 8704085, 2177591, 154772, 2349, 7
OFFSET
1,5
COMMENTS
A minimal edge cover is an edge cover such that the removal of any edge in the cover destroys the covering property. Equivalently, these are the edge covers whose connected components are stars. A minimal edge cover is not the same as a minimum edge cover.
LINKS
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Minimal Edge Cover
EXAMPLE
Table starts:
================================================================
m\n| 1 2 3 4 5 6 7
---|------------------------------------------------------------
1 | 0 1 1 1 2 2 3 ...
2 | 1 2 6 17 45 120 324 ...
3 | 1 6 38 190 1021 5494 29042 ...
4 | 1 17 190 1834 19988 208186 2177591 ...
5 | 2 45 1021 19988 419710 8704085 179649371 ...
6 | 2 120 5494 208186 8704085 356269056 14484264119 ...
7 | 3 324 29042 2177591 179649371 14484264119 1163645044100 ...
...
CROSSREFS
Main diagonal is A288027.
Rows 1-3 are A182097, A288029, A288030.
Cf. A286912.
Sequence in context: A008300 A321789 A173887 * A137376 A039761 A196073
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jun 04 2017
STATUS
approved