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#1 2009-10-25 00:36:05

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Interesting pattern


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#2 2009-10-25 01:11:55

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Interesting pattern




Hence, if n is the number of 1’s,

Now




Thus

Hence we have the required formula

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Last edited by JaneFairfax (2009-10-25 01:20:57)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#3 2009-10-25 05:45:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,432

Re: Interesting pattern

Hi Jane;

Isn't it unfortunate the a_n do not continue a predictable pattern. I know you did not say they did. Just looking at your stuff.

Last edited by bobbym (2009-10-25 05:53:04)


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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#4 2009-10-25 06:37:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,432

Re: Interesting pattern

Hi Jane;

A recurrence like this, is similar to a full history recurrence. They are easy to solve:

Theorem: Every full history recurrence can be changed into a finite history recurrence by the method of differences.

Form a new recurrence:

Now subtract them and you have a finite history recurrence.

Last edited by bobbym (2009-10-25 09:55:40)


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

#5 2009-10-25 15:46:04

soroban
Member
Registered: 2007-03-09
Posts: 452

Re: Interesting pattern

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