# [seqfan] Re: Q about magic squares as produced by Matlab

israel at math.ubc.ca israel at math.ubc.ca
Tue Oct 27 23:59:57 CET 2015

```This is a known issue with Matlab's "magic". The Matlab help file for magic
states:

-----------------------------
M = magic(n) returns an n-by-n matrix
constructed from the integers 1 through n^2 with
equal row and column sums. The order n must be a scalar greater than
or equal to 3.

...

Limitations
If you supply n less than 3, magic returns
either a nonmagic square, or else the degenerate magic squares 1 and [].
---------------------------------

In fact magic(2) returns the matrix

[ 1 3 ]
[ 4 2 ]

which does have determinant -10.

I guess we could insert the value -10, changing the Name to
"a(n) is the determinant of the matrix returned by the Matlab
command magic(n)", with a comment to the effect that for n=2 this
is not a magic square.  Or delete the 1 (on the grounds that Matlab
says n must be >= 3) and make the offset 3.

Cheers,
Robert

On Oct 27 2015, Neil Sloane wrote:

>Dear Seqfans, Sequence A160523 is
>a(n) is the determinant of the magic square of order n produced by Matlab.
>1, -360, 0, 5070000, 0, -348052801600
>Offset 1 (which must be wrong)
>(Matlab) det(magic(n));
>
>I just received an email from someone saying:
>
>"det(magic(2)) = -10 and maybe a(2) should be added the sequence."
>
> and giving the matrix
>1 3
>
>4 2
>
>- which of course is not a magic square of order 2. There are no magic
>squares of order 2. But maybe Matlab thinks there are.
>
>There is clearly something wrong with A160253.
>
>Could someone who has access to Matlab kindly check it?
>
>
>Best regards
>Neil
>
>Neil J. A. Sloane, President, OEIS Foundation.
>11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>Phone: 732 828 6098; home page: http://NeilSloane.com
>Email: njasloane at gmail.com
>
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>
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>
>
```