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%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
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