cp's OEIS Frontend

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.

%I A056787 #22 Jul 02 2025 16:02:00
%S A056787 1,2,6,40,303,2929,29752,316935
%N 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.
%C A056787 a(n)>=A056841(n) since the trees of A056841 are a subset of these here. Edges along diagonals may cross.
%H A056787 M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>
%H A056787 R. J. Mathar, <a href="/A056787/a056787.cpp.txt">C++ program</a>
%H A056787 R. J. Mathar, <a href="/A056787/a056787.txt">Polyforms (ASCII art)</a>
%e A056787 For n=2 we have
%e A056787 o-o
%e A056787 and
%e A056787 ..o
%e A056787 ./.
%e A056787 o..
%e A056787 as the only a(2)=2 candidates. Trees contributing to n=7 are
%e A056787 o.o-o
%e A056787 |\.\.
%e A056787 o.o-o
%e A056787 ...\.
%e A056787 ....o
%e A056787 or
%e A056787 o....
%e A056787 |\...
%e A056787 o.o-o
%e A056787 ...X.
%e A056787 ..o.o
%e A056787 ./...
%e A056787 o....
%e A056787 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 A056787 See also A056840, A056841.
%K A056787 nonn,more
%O A056787 1,2
%A A056787 _James Sellers_, Aug 28 2000
%E A056787 Edited by _R. J. Mathar_, Apr 13 2006
%E A056787 a(7)-a(8) from _Sean A. Irvine_, May 11 2022