A056787 - OEIS

%I #21 May 11 2022 16:20:20

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

%N 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.

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

%H M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>

%H R. J. Mathar, <a href="/A056787/a056787.cpp.txt">C++ program</a>

%H R. J. Mathar, <a href="/A056787/a056787.txt">Polyforms (ASCII art)</a>

%e For n=2 we have

%e o-o

%e and

%e ..o

%e ./.

%e o..

%e as the only a(2)=2 candidates. Trees contributing to n=7 are

%e o.o-o

%e |\.\.

%e o.o-o

%e ...\.

%e ....o

%e or

%e o....

%e |\...

%e o.o-o

%e ...X.

%e ..o.o

%e ./...

%e o....

%e 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.

%Y See also A056840, A056841.

%K nonn,more

%O 1,2

%A _James A. Sellers_, Aug 28 2000

%E Edited by _R. J. Mathar_, Apr 13 2006

%E a(7)-a(8) from _Sean A. Irvine_, May 11 2022