A336281 Total number of ways of embedding connected graphs with n edges in the square lattice with diagonals allowed.

2, 6, 41, 318, 3108, 32243, 350575, 3896568

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: A319633 A367365 A367603 * 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