Notation for a "conditional" set

Question

Is there any commonly used short notation for the following?

$A_n = \begin{cases} \{a_n\}, & \text{if $n$ is odd} \\ \emptyset, & \text{if $n$ is even} \end{cases} $

I'm looking for something like $A_n = \{a_n\}_{[\text{$n$ is odd}]}$ that will fit on one row.

Answer 1

Maybe use a Kronecker delta/indicator function. But "0" would have to be interpreted set theoretically to be $\{\}$.

Answer 2

If you use the indicator function (that I note $1_A$) then you can write it $$ a_n 1_{2\nmid n}\ \ \ \ \ \ a_n 1_{ 2\Bbb Z+1}(n) $$