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User: James W. Anderson

James W. Anderson has authored 1 sequences.

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

James W. Anderson, Jul 15 2020

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'.

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.]

Without diagonal edges, we get A019988.

Cf. A052436.

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

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User: James W. Anderson

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

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