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#1 2014-05-20 15:41:43

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,891
Website

What is the gf of...

In how many ways can you add 1,2 and 3 to get 8? (order matters)

Here is the list of all 81 ways:

What is the gf that I need for this problem?


'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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#2 2014-05-20 15:59:17

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,672

Re: What is the gf of...

One way is by using a couple of gf"s

G(x,3) = 3

G(x,4) = 19

G(x,5) = 30

G(x,6) = 21

G(x,7) = 7

G(x,8) = 1

now add em up!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2014-05-20 16:12:05

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,891
Website

Re: What is the gf of...

Thank You


'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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#4 2014-05-20 16:15:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,672

Re: What is the gf of...

The search is now on for a single gf? I have to go eat so I will not find it.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#5 2014-05-20 16:26:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,658

Re: What is the gf of...

Hi guys

I have found this to be the gf from bobbym's gf:


“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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#6 2014-05-20 16:28:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,672

Re: What is the gf of...

Hi;

Very nice!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#7 2014-05-20 16:33:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,658

Re: What is the gf of...

Thanks. It directly follows from your gf, because we need to sum up all of the gf's for different n's.


“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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#8 2014-05-20 16:37:34

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,658

Re: What is the gf of...

Another way you can get the GF is by noticing that the numbers follow the recurrence:


“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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#9 2014-05-20 17:08:12

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,891
Website

Re: What is the gf of...

How does the reccurence help me find the gf?


'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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#10 2014-05-20 19:18:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,672

Re: What is the gf of...

You can go from the recurrence to the gf and back again.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#11 2014-05-20 20:02:49

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,891
Website

Re: What is the gf of...

How?


'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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#12 2014-05-20 20:29:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,672

Re: What is the gf of...

Experimentally of course!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#13 2014-05-21 01:04:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,658

Re: What is the gf of...

Bobbym has a thread on how to get the GF of the Fibonacci numbers experimentally. Look over there.


“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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#14 2014-05-21 01:17:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,672

Re: What is the gf of...

These are the Tribonacci numbers.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#15 2014-05-21 01:47:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,658

Re: What is the gf of...

I know.


“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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#16 2014-05-21 01:52:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,672

Re: What is the gf of...

Would you agree that getting a closed form for them is very difficult?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#17 2014-05-21 02:12:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,658

Re: What is the gf of...

For whom?


“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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#18 2014-05-21 02:24:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,672

Re: What is the gf of...

The tribonacci numbers.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#19 2014-05-21 02:29:17

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,658

Re: What is the gf of...

I do agree.


“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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#20 2014-05-21 03:12:17

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,891
Website

Re: What is the gf of...

How can I look it up?


'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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#21 2014-05-21 03:14:46

ShivamS
Member
Registered: 2011-02-07
Posts: 3,629

Re: What is the gf of...

I think by using a search engine.

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#22 2014-05-21 03:34:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,672

Re: What is the gf of...

How can I look it up?

You do not need to look it up.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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