How do I formulate a specific formula for this sequence?

Question

I was doing research on whether an equation can be formed about the Mobius Strip on the basis of how many times it is cut (thirds, fourths, fifths, etc.). I started with 0 cuts. This is what I got: 0 cuts, 0 two-sided loops.. 1 cut, 0 2 sided loops. 2 cuts, 1 2-sided loop, 3 cuts, 2 2-sided loops. 4 cuts, 2 2-sided loops. Essentially, the equation is; 0,0,1,2,2,3,3,4,4,5,5, etc. How can I find an equation or formula where 'n' is the amount of cuts? It is not linear,quadratics, cubic, in powers or even Paschal's triangle. Is it possible to formulate a formulate in my context?

Answer 1

It's pretty easy to see that the formula $\lceil \frac{n}2\rceil$ "almost" gives the correct sequence. The only case it doesn't handle is $n=1$. So one can augment the formula a bit to take care of that case: $(\lceil \frac{n}2\rceil)\mathrm{sgn}(n-1)$ takes care of $n=1$. ($\mathrm{sgn}$ is the sign function). Because $\mathrm{sgn}(n-1)$ gives -1 if $n=0$, we need to check that case. Fortunately $\mathrm{sgn}(-1)(\lceil \frac02\rceil)=0$.