What is the notation for a stepped range

Question

I am searching for a notation which represents a (closed) integer range in certain steps.

A step size of 4 in the interval $[-4\ldotp\ldotp 12]$ would produce: $\{-4,0,4,8,12\}$

Answer 1

The only thing that springs to mind for me is something like this: $$\big\{4k\mid k\in\{-1,0,...,3\}\big\} $$

Otherwise, you may have to define your own notation.

Answer 2

I was also looking for a standard math notation. In programming, it's typical to see things like this:

$$\text{−4 <= n <= 12, step 4}$$

$$\text{ for −4 to 12, step 4}$$

I also like the idea of simply expanding the existing range notation to accept a step value as a final parameter. Expanding on Eff's answer, I'm guessing that defining such a notation would go something like this:

$$f( a, z, i ) = \text{}[ a…z \text{, } i ] = \{ i ∣ ∈ \{ a, …, z \} \} $$ $$∴$$ $$\text{[−4…12, 4] = {−4,0,4,8,12} }$$