I have just spent a lot of time trying to find the official Alhambra ticket site. FINALLY, I found it and thought I would post it here, since so many of the sites that google takes you to are sites where you buy a guided tour from a private company that includes the entrance ticket.
I think this is the site.
https://tickets.alhambra-patronato.es/en/tickets-alhambra-general/
If I am wrong, let me know. Looks like tickets are available only through January (and some January dates are close to being sold out), so there must be a three month window.
Buen camino, Laurie