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Topic: How many rectangles are in an n by n square array of dots?
Replies: 4   Last Post: Sep 9, 2006 11:14 PM

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 Joshua Zucker Posts: 1,450 Registered: 1/30/05
Re: How many rectangles are in an n by n square array of dots?
Posted: Sep 9, 2006 6:54 PM

On 9/9/06, Oliver Stemforn <olive79pop@yahoo.com> wrote:
> To:
>
> Lou Talman
> Department of Mathematical and Computer Sciences
> Metropolitan State College of Denver
>
>
> You are wrong about me having to be more careful when a rectangle counts. In the description for this problem, I never limited the orientation of the rectangles I was seeking to be counted within an array. I stated to get a count for the total. If I had only wanted a total of vertical/horizontal rectangles, I would have had to mention that explicitly. Or if I had wanted only a total of oblique rectangles, I would have had to mention that explicitly.
>

The original question was:
>Can you come up with a polynomial in terms of n for the total number
of rectangles for a general n by n array?

I think the implication is that if you wanted a polynomial, you should
have been more careful in your choice of problem.

See
http://www.research.att.com/~njas/sequences/A085582
for example.
--Joshua Zucker

Date Subject Author
9/8/06 Oliver Stemforn
9/9/06 talmanl@mscd.edu
9/9/06 Oliver Stemforn
9/9/06 Joshua Zucker
9/9/06 Oliver Stemforn