[seqfan] Wiener index of n X k grid
Ed Jeffery
lejeffery7 at gmail.com
Tue Jan 17 20:51:25 CET 2012
I'd like to have another opinion before submitting a correction to the
following sequence.
Sequence A143368={0,1,8,4,25,72,...} is defined as a triangle read by rows
in which entry T(n,k) gives the Wiener index of a n X k grid, 1<=k<=n.
Since an index T(n,k)=0 if and only if either n=0 or k=0, then either the
initial term (= 0) of this sequence should be deleted (since by definition
0 < any n or k) or the triangle should be defined for 0<=k<=n and rewritten
as
0
0,1
0,8,4
0.25,72,10
....
giving the sequence {0,0,1,0,8,4,...} with offset 0,5. But the left column
sequence = {0,0,...} of the above triangle is useless and should be deleted
leaving the triangle
T(n,k)=
1
8,4
25,72,10
...
read by rows from the proposed corrected sequence {1,8,4,25,72,10,...},
with 1<=k<=n and offset 1,2.
Finally, the current version of A143368 gives (if I'm not mistaken) the
triangle
0
1,8
4,25,72
...
which is clearly incorrect: for example, it can be shown that the Wiener
index for a n X 1 grid (n>=1) is given by the sequence {1,8,25,...}, which
is column 1 of the proposed corrected version of the triangle.
Ed Jeffery
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