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Rob_Gandy

Can you find a closed form equation for the sequence?

Question

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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4 answers to this question

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Is a(n) = ⌊n/3⌋ (where ⌊x⌋ stands for

floor function) closed enough?
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I'm assuming you can't use floor or mod?

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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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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

post-14842-0-79671500-1359182692_thumb.p

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