OFFSET
1,2
COMMENTS
Begin and end on the same node, but do not include the ending step in the sum.
Two isomorphic trees will always have the same alternating sum, because flipping branches around will always switch two odd-length sequences separated by another odd-length sequence (the reverse is NOT true in general - flipping sequences around is not even guaranteed to create a tree).
Trees which are symmetric around an edge will have alternating sum 0, because the same numbers appear on either side of that edge.
Two graphs can have the same alternating sum, and the same sum, and still not be isomorphic.
EXAMPLE
For the tree of length 2, 1-2+1-2 = -2. The tree is described by [1,2,1,2].
First five rows of the triangle:
0
2
0, 6
2, 4, 12
0, 2, 6, 10, 20
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Michael Arnold, Jun 23 2020
STATUS
approved