A335790 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.

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, 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, 14, 16, 18, 20, 22, 24, 26, 28, 30, 34, 36, 38, 42, 54, 72

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.

Links

Table of n, a(n) for n=1..70.

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

Sequence in context: A140876 A243997 A036044 * A078991 A346790 A217572

Adjacent sequences: A335787 A335788 A335789 * A335791 A335792 A335793

Keyword

nonn,tabf

Author

Michael Arnold, Jun 23 2020

Status

approved