# [seqfan] n x n matrices with adjacent entries differing by +/- 1

Edwin Clark eclark at math.usf.edu
Mon Oct 27 23:41:58 CET 2008

```On Mon, 27 Oct 2008, Benoît Jubin wrote:

> It would also be interesting to consider the entries of the matrix in
> Z/kZ (that is, 1 and k would also differ by 1). And also the same
> sequence for entries in Z or N, the upper-left term being 0.
>

Benoit:

The latter suggestion is actually more in the spirit of the problem that
made me think of these sequences: Namely the Problem of the Month for
mathematics students here at the University of South Florida:

A number of coins are placed on each square of a checkerboard such tha the
amounts on every two squares having a common side differ by one cent.
Give that the amount on one spare is 3 cents and another is 17 cents, find
the total amount of money on both diagonals. [Don't post an answer since
the problem is not due yet. :-)]

This problem was found by my colleague Mile Krajcevski in
a little booklet "Quantum Quandaries" (100 Brainteasers from QUANTUM ,
the magazine of math and science) , published in 1996 by the National
Science Teachers Association . The author of this problem is V.Proizvolov

Many similar questions can be raised. No need to restrict to nxn matrices
try for n x m matrices or indeed replace the n x m grid by any graph.

I looked particularly at several n x 1 cases for various sets of entries
and found some essentially identical sequences, but not with the same
definition.

This seems a rather natural question. One can also look at the case where
all entries differ by +/- q for different values of q. There is no end to
it.

--Edwin

```