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#1 2013-11-29 06:49:30

Nils-Ake
Member
Registered: 2008-04-15
Posts: 20

n^2

big_smile I have just realized




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#2 2013-11-29 07:04:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: n^2

Hi;

From your table we get the difference equation,

with

when solved for we get


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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#3 2013-11-29 13:24:43

Nils-Ake
Member
Registered: 2008-04-15
Posts: 20

Re: n^2

Thanks bobby smile I think the symmetry is pretty cool!

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#4 2013-11-29 14:01:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: n^2

Hi;

I do not know whether it is original but I have never seen it put like that so thanks for posting it.


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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#5 2013-11-29 14:14:33

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,172
Website

Re: n^2

bobbym wrote:

Hi;

From your table we get the difference equation,

with

when solved for we get

What does this mean?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#6 2013-11-29 14:16:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,237

Re: n^2

Take a look at the table he constructed and think iteratively.


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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#7 2013-11-29 21:06:34

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,426

Re: n^2

hi Nils-Ake

Many of my posts have diagrams.  Here's one for your discovery.  smile

Bob

View Image: nils.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#8 2013-11-29 23:21:35

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 615
Website

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#9 2013-12-03 04:09:06

antonrasmussen
Member
Registered: 2013-11-25
Posts: 16

Re: n^2

Interested to hear more on how you stumbled onto this . . . were you working on something? Playing around?

Also, this seems to relate to Pascal's triangle . . . is there a connection there?


-Anton


--
Noobdunno

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