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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

What's the formula for the number of those squares???

*Last edited by anonimnystefy (2012-02-11 03:22:18)*

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi anonimnystefy;

Could you tell me the link please?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

Did you construct a table of the small values by hand?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

nope.imma gonna.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

here?

i have found that subtracting the 4th difference of the numbers gives 2,2,2,2,...

so we have: a_n=An^4+Bn^3+Cn^2+Dn+E.we can easily find those but what has actually been bothering me is the same tak but only on an m x n grid.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Whoa! How about letting me see you sequence first? The one you got empirically.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

n |a_n

--------

1 | 0

2 | 1

3 | 6

4 | 20

5 | 50

6 | 105

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Now you actually did those by hand? Drawing tiny little squares until your fingers bled.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

didn't do it for 6,but after finding the 3rd differences i saw that they were all squares.but i can easily check for 6.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

First things first. I notice your sequence is shifted. You can adjust that.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

i used 1x1 grid to be just a dot.seemed more logical.

2x2 was this:

. .

. .

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hmmmm, but the problem as outlined uses the convention of counting interior squares and not lattice points. Since we are counting squares do you not now think that it is more consistent to set the problem up in terms of squares?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

ok,then just shift the whole sequence by one to the left.

*Last edited by anonimnystefy (2012-02-11 09:12:47)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Kayrect! Now what would you do to go about getting a formula, remember to shift your list first.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

???

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

so we have: a_n=An^4+Bn^3+Cn^2+Dn+E.we can easily find those

From here.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

but it's better to expand that.get a better form for working with it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Maybe, but that form makes you look like a combinatorial genius. People will be in awe of you.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

maybe,but i know that you're a combinatorial genius,so you don't have to prove it.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

When I was 4 I was rated with the IQ of a genius. But now that I am 9, I am rated as an imbecile.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

i'm happy for you.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Thanks, I am happy for me too. Now people come by and pat me on the head and tell me there will someday be a cure.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

what about an mxn grid,i.e a rectangular grid?

*Last edited by anonimnystefy (2012-02-12 04:11:14)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

For that I have:

I do not know if it is correct. Perhaps you would like to test it?

Break time! Pass me the pancakes!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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