How to represent this sequence mathematically?

Question

I need to represent the sequence of pairs $$(N,0), (N-1,1), (N-2,2), \ldots , \left( \frac{N}{2}, \frac{N}{2}\right) $$ in a way I can use in a formula. Is there any way to do this? Thanks!

Answer 1

What about

$$(N-i,i),\quad i\in\{0,1,\ldots N/2\}$$

(assuming $N$ is even)?

Answer 2

$$a_n=(N-n,n)\forall n\in\left[0,\dfrac{N}{2}\right],N\in\{2k:k\in\mathbb{Z}\}$$