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.