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**Dab Alex****Guest**

I have a problem I need to solve so I'd need an answer or a way to solve it.

I need to find out the number of combinations of 6 numbers from 49 numbers. The tricky part (for me )is that I want to exclude the combinations of numbers that are in sequence of minimum 3 meaning:

I want to exclude results like {1,2,3,4,5,6} or like {1,2,3,9,12,14} or {1,2,3,4,6,8} so on....

Thank you!

**Dab Alex****Guest**

I forgot to mention.... without repetitions and order is not important

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hi;

If order does not count then doesn't {2,46,31,1,5,3} have to excluded? There is a {1,2,3} in there.

*Last edited by bobbym (2013-02-19 14:53:23)*

**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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**Dab Alex****Guest**

I mean that the sequence of consecutive numbers must not be contained in the result so this result {2,46,31,1,5,3} must also be excluded.

I specified that order is not important because no. of combinations if order is important is 1.00683475e+10 and if it isn't no. of combinations is 13983816

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hi;

Yes, you are correct there are 10068347520 permutations and only 13983816 combinations.

I think I have enough to start working on it, thanks.

I am getting that 13316842 out of 13983816 do not have 3 or more numbers in sequence. This agrees well with simulations.

*Last edited by bobbym (2013-02-21 04:50:49)*

**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 the reccurence is:

A(n,k)=A(n-3,k-2)+A(n-2,k-1)+A(n-1,k), n>3, with the appropriate starting conditions.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hmmmm? Are you sure?

**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

Preety much.

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: 85,347

What are your initial conditions?

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

A(n,k) is 0 for n<=0, except A(0,0)=1.

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: 85,347

You also did not define n or k. What are they?

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

Numbers, of course.

Joke aside, n is how many numbers we choose from and k is how many numbers we choose.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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k is how many numbers we choose.

You are saying n=6 and k is the number of consecutives?

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

No. n=49 and k=6.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Did you check it by actually running the recurrence? Does it get my answer?

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

Sorry. Take A(0,1)=1 as well.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hi;

The same question as the last post. Did you try it?

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'm calculating it. It will take a while.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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That is like music to my ears!

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

Do you think there is a way to speed it up?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

I do not know what you are doing, so how can I say.

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 am just running the recurrence.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

That is what I mean. In Maxima?

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: 85,347

Well, when I ask this question the kaboobly doo will hit the fan. Where does it come from?

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**