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.

1, 2, 6, 40, 303, 2929, 29752, 316935

Offset

1,2

Comments

a(n)>=A056841(n) since the trees of A056841 are a subset of these here. Edges along diagonals may cross.

Links

Table of n, a(n) for n=1..8.

M. Vicher, Polyforms

R. J. Mathar, C++ program

R. J. Mathar, Polyforms (ASCII art)

Example

For n=2 we have
o-o
and
..o
./.
o..
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.

Crossrefs

See also A056840, A056841.

Sequence in context: A354313 A351739 A098854 * A098852 A274482 A274277

Adjacent sequences: A056784 A056785 A056786 * A056788 A056789 A056790

Keyword

nonn,more

Author

James A. Sellers, Aug 28 2000

Extensions

Edited by R. J. Mathar, Apr 13 2006

a(7)-a(8) from Sean A. Irvine, May 11 2022

Status

approved