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Can you find a closed form equation for the sequence?


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4 replies to this topic

#1 Rob_Gandy

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Posted 25 January 2013 - 12:11 AM

This problem recently popped back into my head. In one of my college calculus classes while working on sequences we came across the sequence 0,0,1,1,2,2,3,3,4,4,... and if I remember correctly we were told there was no closed form equation for it. But, I found one and presented it to the class.

a[n]=(2n-1+(-1)n)/4  n=0...infinity

 

My question is: Is there a closed form equation to define the sequence 0,0,0,1,1,1,2,2,2,3,3,3....? If not, why not?

 

Just wondering.  :D


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#2 witzar

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Posted 25 January 2013 - 04:34 PM

Spoiler for ...


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#3 vinay.singh84

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Posted 25 January 2013 - 09:03 PM

I'm assuming you can't use floor or mod?


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#4 Rob_Gandy

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Posted 25 January 2013 - 09:47 PM

I'm assuming you can't use floor or mod?

If it can be done without them I'd like to see it.


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#5 bushindo

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Posted 26 January 2013 - 07:45 AM

This problem recently popped back into my head. In one of my college calculus classes while working on sequences we came across the sequence 0,0,1,1,2,2,3,3,4,4,... and if I remember correctly we were told there was no closed form equation for it. But, I found one and presented it to the class.
a[n]=(2n-1+(-1)n)/4  n=0...infinity
 
My question is: Is there a closed form equation to define the sequence 0,0,0,1,1,1,2,2,2,3,3,3....? If not, why not?
 
Just wondering.  :D

 

Here's one that doesn't use floor or mod

Spoiler for


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