

A336281


Total number of ways of embedding connected graphs with n edges in the square lattice with diagonals allowed.


2




OFFSET

1,1


COMMENTS

The embedding must map edges in the graph onto either horizontal or vertical grid lines of length 1 or diagonals of length sqrt(2). Vertices in the graph must map onto lattice points, and of course must preserve the incidence structure of the graph. A square in the lattice may have both diagonals present  their intersection does not count as an incidence.
Configurations differing only a rotation or reflection are not counted as different.
The resulting figures are variously called 'polysticks', 'polyedges' or 'polyforms'.


LINKS

Table of n, a(n) for n=1..8.
N. J. A. Sloane, Illustration for a(1)=2, a(2)=6, a(3)=41. [Thanks to Peter Munn for correcting errors in my first drawing.]


CROSSREFS

Without diagonal edges, we get A019988.
Cf. A052436.
Sequence in context: A118623 A000612 A319633 * A326268 A096138 A004153
Adjacent sequences: A336278 A336279 A336280 * A336282 A336283 A336284


KEYWORD

nonn,hard,more,nice


AUTHOR

James W. Anderson, Jul 15 2020


EXTENSIONS

a(7)a(8) from John Mason, Aug 17 2021


STATUS

approved



