%I #16 Aug 13 2020 21:57:44
%S 0,2,0,6,2,4,12,0,2,6,10,20,0,2,4,6,8,10,12,18,30,0,2,4,6,8,10,14,16,
%T 20,28,42,0,2,4,6,8,10,12,14,16,18,22,24,26,30,40,56,0,2,4,6,8,10,12,
%U 14,16,18,20,22,24,26,28,30,34,36,38,42,54,72
%N Triangle read by rows of possible absolute values of alternating sums when traveling around a tree with n edges, with each node labeled with the number of edges connected to it, until each edge has been visited twice.
%C Begin and end on the same node, but do not include the ending step in the sum.
%C Two isomorphic trees will always have the same alternating sum, because flipping branches around will always switch two oddlength sequences separated by another oddlength sequence (the reverse is NOT true in general  flipping sequences around is not even guaranteed to create a tree).
%C Trees which are symmetric around an edge will have alternating sum 0, because the same numbers appear on either side of that edge.
%C Two graphs can have the same alternating sum, and the same sum, and still not be isomorphic.
%e For the tree of length 2, 12+12 = 2. The tree is described by [1,2,1,2].
%e First five rows of the triangle:
%e 0
%e 2
%e 0, 6
%e 2, 4, 12
%e 0, 2, 6, 10, 20
%K nonn,tabf
%O 1,2
%A _Michael Arnold_, Jun 23 2020
