[Math] Odd-Odd-Even-Even Sequence

Question

I want a sequence that alternates between being an even integer and being an odd integer and I've come up with this sequence $ s_n=\lfloor \frac{n}{2} \rfloor $. So, it goes $0,1,1,2,2,3,3,\ldots$ and I was wondering if I can do something similar without using a floor or ceiling function. The important thing is that it goes back and forth between even and odd without simply alternating.

Answer 1

The sum of the first $n$ integers, giving $n(n+1)/2$, is a simple example: $$1,3,6,10,15,21,28,36,45,55,\ldots$$