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

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preface (intro) :
How many rectangles within a Square (grid) ?
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How many rectangles (are there) within a Steps-Grid ?

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[Ilan Mayer]

Post by ***@gmail.com
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

Post by ***@gmail.com
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

[[e-mail]]

Post by Ilan Mayer

Post by ***@gmail.com
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

Post by ***@gmail.com
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 )