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A336281 Total number of ways of embedding connected graphs with n edges in the square lattice with diagonals allowed. 2
2, 6, 41, 318, 3108, 32243, 350575, 3896568 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 22 21:47 EST 2022. Contains 350504 sequences. (Running on oeis4.)