

A019988


Number of ways of embedding a connected graph with n edges in the square lattice.


4



1, 2, 5, 16, 55, 222, 950, 4265, 19591, 91678, 434005, 2073783, 9979772, 48315186, 235088794, 1148891118, 5636168859
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OFFSET

1,2


COMMENTS

These are referred to as 'polysticks', 'polyedges' or 'polyforms'.  Jack W Grahl, Jul 24 2018


REFERENCES

Brian R. Barwell, "Polysticks," Journal of Recreational Mathematics 22 (1990), 165175.


LINKS

Table of n, a(n) for n=1..17.
D. Goodger, An introduction to Polysticks
M. Keller, Counting polyforms
D. Knuth, Dancing Links, arXiv:cs/0011047 [cs.DS], 2000. (A discussion of backtracking algorithms which mentions some problems of polystick tiling.)
Ed Pegg, Jr., Illustrations of polyforms
Eric Weisstein's World of Mathematics, Polyedge [From Eric W. Weisstein, Apr 24 2009]


CROSSREFS

If only translations (but not rotations) are factored, consider fixed polyedges (A096267).
If reflections are considered different, we obtain the onesided polysticks, counted by (A151537).  Jack W Grahl, Jul 24 2018
Sequence in context: A149972 A026106 A066642 * A137732 A057973 A102461
Adjacent sequences: A019985 A019986 A019987 * A019989 A019990 A019991


KEYWORD

nonn,nice,hard,more


AUTHOR

Russ Cox


EXTENSIONS

More terms from Brendan Owen (brendan_owen(AT)yahoo.com), Feb 20 2002
Additional references from Jack W Grahl, Jul 24 2018


STATUS

approved



