You can see this as sampling z(z+1)/2 times sorta-independently, or as sampling z2 times with less independence (ie most sums are sampled twice).
Either view works, and as you said, it doesn’t change the outcome.
You can see this as sampling z(z+1)/2 times sorta-independently, or as sampling z2 times with less independence (ie most sums are sampled twice).
Either view works, and as you said, it doesn’t change the outcome.