novaBBS - rec.puzzles - Re: How many rectangles (are there) within a Steps-Grid ?

How many rectangles (are there) within a Steps-Grid ?

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Subject: How many rectangles (are there) within a Steps-Grid ?
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by: henh...@gmail.com - Wed, 5 Oct 2022 01:01 UTC

Re: How many rectangles (are there) within a Steps-Grid ?

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Subject: Re: How many rectangles (are there) within a Steps-Grid ?
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by: Ilan Mayer - Wed, 5 Oct 2022 01:48 UTC

Re: How many rectangles (are there) within a Steps-Grid ?

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Subject: Re: How many rectangles (are there) within a Steps-Grid ?
From: henha...@gmail.com (henh...@gmail.com)
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by: henh...@gmail.com - Wed, 5 Oct 2022 02:08 UTC

On Tuesday, October 4, 2022 at 6:49:01 PM UTC-7, Ilan Mayer wrote:
> On Tuesday, October 4, 2022 at 9:01:30 PM UTC-4, henh...@gmail.com wrote:
> > preface (intro) :
> > How many rectangles within a Square (grid) ?
> > https://i.stack.imgur.com/qLvdX.png
> See https://oeis.org/search?q=1%2C9%2C36%2C100%2C225%2C441&sort=&language=english&go=Search
> > How many rectangles (are there) within a Steps-Grid ?
> >
> > https://i.imgur.com/VdaWWwX.png
> See https://oeis.org/search?q=1%2C5%2C15%2C35%2C70&sort=&language=english&go=Search

thanks...

So for the Steps-Grid consisting of 3 small squares,
the answr is 5 = (5C4)

The other answers are (6C4), (7C4), (8C4), (9C4), ...

the questio is... Is ther a simple, intuitive way to get at these (n+2 C 4) ?

( a clever man came with it a few months ago
------- maybe this was pretty much unknown earlier )

Ontogeny recapitulates phylogeny.

interests / rec.puzzles / Re: How many rectangles (are there) within a Steps-Grid ?

Subject	Author
How many rectangles (are there) within a Steps-Grid ?	henh...@gmail.com
Re: How many rectangles (are there) within a Steps-Grid ?	Ilan Mayer
Re: How many rectangles (are there) within a Steps-Grid ?	henh...@gmail.com