A288027 Number of minimal edge covers in the grid graph P_n X P_n.

0, 2, 38, 1834, 419710, 356269056, 1163645044100, 15000387107144576, 749707067231291403016

Offset

1,2

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.

Links

Table of n, a(n) for n=1..9.

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Minimal Edge Cover

Example

In the 3 X 3 grid, the minimal edge covers up to rotation and reflection are:
.__.__.    .__.__.    .__.__.    .__.__.    .__.__.    .__.  .
.__.__.    .  .  .    .__.  .    .  .__.    .  |  .    .  |  |
.__.__.    |  |  |    .__.  |    |__.  |    |  .__|    |  .__.
The first two of these need to be counted 2 and 4 times and the rest which have no symmetry 8 times so a(3) = 38.

Crossrefs

Main diagonal of A288025.

Cf. A286913.

Sequence in context: A187544 A187545 A246484 * A184994 A334554 A348162

Adjacent sequences: A288024 A288025 A288026 * A288028 A288029 A288030

Keyword

nonn,more

Author

Andrew Howroyd, Jun 04 2017

Extensions

a(1) corrected by Andrew Howroyd, Jan 29 2023

Status

approved