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A056787
Number of incongruental unlabeled undirected trees with n nodes on a square lattice and edges of length 1 or sqrt(2) admitted to the 4 nearest or 4 2nd nearest neighbors.
as the only a(2)=2 candidates. Trees contributing to n=7 are
o.o-o
|\.\.
o.o-o
...\.
....o
or
o....
|\...
o.o-o
...X.
..o.o
./...
o....
where dashes are edges in E, NE, N, NW, W, SW, S or SE direction that connect nodes marked 'o' horizontally, vertically or along diagonals, and X's are crossing diagonal edges.