Can you find a closed form equation for the sequence?

[Rob_Gandy]

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.

[witzar]

Is a(n) = ⌊n/3⌋ (where ⌊x⌋ stands for

floor function) closed enough?

[vinay.singh84]

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

[Rob_Gandy]

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

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

[bushindo]

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.

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