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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,511

Hi;

Perhaps, the other was too personal of a question. I have no problem with what you are.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Meh.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,511

Hmmmm. There is that word again.

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**If it ain't broke, fix it until it is.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Meh. By the way, sorry for hijacking this thread.

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Hi everyone;

I notice that in Pascal's square I can begin with every number instead 1 And the numbers of the square are exponents of 2 multiplied by that numbers. Here an example with 3:

3 3 6 12 24 48 96

3 3 6 12 24 48 96

6 6 12 24 48 96 192

12 12 24 48 96 192 384

24 24 48 96 192 384 768

48 48 96 192 384 768 1536

96 96 192 384 768 1536 3072

Which is the result of

3x1 3x1 3x2 3x4

3x1 3x1 3x2 3x4

3x2 3x2 3x4 3x8

3x4 3x4 3x4 3x16

*Last edited by Mpmath (2012-10-30 02:24:39)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,511

Hi Mpmath;

Sorry I could not get to you before but I had much work. Okay, also your columns are what is called a full history recurrence.

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**If it ain't broke, fix it until it is.**

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Thanks bobbym.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,511

Hi;

Have you tried primes in the top row?

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

I tried. This is the result:

2 3 5 7 11

2 3 5 7 11

4 6 10 14 22

8 12 20 28 44

16 24 40 56 88

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,511

Hi;

And what did you notice?

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

The sum of the numbers of each row doesn't give a right result, but all numbers are the product of the prime and all exponents of 2.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,511

Okay, just wanted to see what happens.

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

I think that the square with prime numbers is not a Pascal's square, but it's still an intersting disposition of numbers.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,919

By what principle do you exactly get each number of the square?

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Hi;

Here is the proceedings:

1

1 = 1

= =

1 = 1

1 + 1 = 2

+ + +

1 + 1 = 2

= = =

2 + 2 = 4

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

It might be interesting to have different rules. For example: add the numbers above, left and diagonal-above-left.

1 1 1 1

1 3 5 7

1 5 13 25

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Of course. There are so many rules that we can use. For example we can only add the numbers in each row, or in each column, using different kinds of successions. These mustn't be just Pascal's square with one rule.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,919

MathsIsFun wrote:

It might be interesting to have different rules. For example: add the numbers above, left and diagonal-above-left.

1 1 1 1

1 3 5 7

1 5 13 25

This seems more in the spirit of Pascal's triangle.

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

The knowledge of some things as a function of age is a delta function.

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Well, this

1 1 1 1

1 3 5 7

1 5 13 25

Is a Pascal's square, similar to the triangle. The rule is the same, but numbers are very different.

*Last edited by Mpmath (2012-10-30 10:28:03)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,511

That one has the rule the one to the left plus the two on top.

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

A Pascal's square has more rules And possibilities than a Pascal's triangle.

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

I also find another square, similiar to that of MathIsFun. The only different is that numbers on the first column and on the first row are exponents of 2. This is the square:

1 1 2 4

1 3 6 12

2 6 15 33

4 12 33 81

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,511

Hi;

What is the rule that is generating each row?

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**If it ain't broke, fix it until it is.**

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**Mpmath****Member**- Registered: 2012-10-11
- Posts: 216

Hi;

Add the numbers above, left and diagonal-above-left, just like the square of MathIsFun. But in mine also the numbers in the first row and in the first column are exponents of 2, obtained by the sum of the numbers.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,511

Hi;

Yes, I see that now, thanks.

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**If it ain't broke, fix it until it is.**

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