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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

I do not know that. But, why would you need to?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

I would like a closed form if possible for that series.

Mind if I ask why you came to this page in the OEIS?

**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
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I looked at his probabilities and compared them to mine, and I saw that they were always almost the same, except for a factor. So I calculated the first few factors and found that they matched that sequence on OEIS. Why?

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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: 85,358

Okay, I was just wondering.

I can get a somewhat closed form for T[5,n] but it is ugly and too complicated you will have to go with the series or the gf.

I will test your 4 conjecture now by simulation.

**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: 15,507

I think it will be easier to extract the coefficient from the GF.

Tell me when you finish the simulations.

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: 85,358

Hi;

I got 11.216568 for 1 million, this is very close to your answer. What do you get for 5?

**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: 15,507

Hi bobbym

15.38578772717056256240736291835039673851, or

in closed form.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: 85,358

I am getting 15.387028 for 1 million, that is again very close. Your answer for 2?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi,

I believe it is;

which matches for n=2,3,4,5

Perhaps we can extract a closed form for that..

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

3.774691358024691358024691358024691358025, which agrees with the dice pdf.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

Hi;

You got 1223 / 324 for 2 ?

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: 15,507

Yes!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

What do you want to do with your solution?

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: 15,507

I do not know? Can we send it to that guy?

I have found the formula for general number of wanted appearences (not just for 2, 3, 4 and 5):

`f(k):=sum(i*(i-k)!/(6^(i-1))*binomial(i-1,k-1)*coeff(ratexpand((sum(x^j/j!,j,0,k-1))^5),x^(i-k)),i,k,6*k-5);`

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

Hi gAr;

I did not see you up there, watch out becuase our latex is damaged and does not display plus signs.

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: 15,507

Didn't see his post either. Looks like gAr and I got the same formula.

*Last edited by anonimnystefy (2013-02-16 06:37:04)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

Hi;

Yes, I can send it or you can send it. Of course it would be with your name on it. Your final form looks like gAr's.

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: 15,507

Hi bobbym

You can send it, but before sending it, please send it to me (in a PM or right here).

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi anonimnystefy and bobbym,

Yes, the final form is the same. I was thinking about egfs and anonimnystefy had a form already. So I started working from there. Maybe we can try for a closed form for some time.

It's late here, see you after a few hours.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

Hi;

I think you should post it first right under where I talk about it in the other thread. That will establish the date.

How will we get latex to him in an email?

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: 15,507

Hi gAr

Maybe you guys can get an asymptotic form if all else fails...

See you later!

Hi bobbym

Which thread?

*Last edited by anonimnystefy (2013-02-16 06:49:07)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

Hi gAr;

See you later. Have a good night.

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: 15,507

Hi bobbym

Which thread?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,358

http://www.mathisfunforum.com/viewtopic.php?id=18866

Be thorough. I will lock the thread after you are done. I am going to take a little break now see you then.

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: 15,507

Thorough? About what?

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