Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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

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

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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)

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

soroban
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Registered: 2007-03-09
Posts: 452

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