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## #1 2009-10-25 23:36:05

JaneFairfax
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### Interesting pattern

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

## #2 2009-10-26 00:11:55

JaneFairfax
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### Re: Interesting pattern

Hence, if n is the number of 1’s,

Now

Thus

Hence we have the required formula

Last edited by JaneFairfax (2009-10-26 00:20:57)

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

## #3 2009-10-26 04:45:25

bobbym

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### 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 (2009-10-26 04:53:04)

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #4 2009-10-26 05:37:17

bobbym

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### 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 (2009-10-26 08:55:40)

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

soroban
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