A288025 Array read by antidiagonals: T(m,n) = number of minimal edge covers in the grid graph P_m X P_n.

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

Andrew Howroyd, Table of n, a(n) for n = 1..153

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

Adjacent sequences: A288022 A288023 A288024 * A288026 A288027 A288028

Keyword

nonn,tabl

Author

Andrew Howroyd, Jun 04 2017

Status

approved