The domain is registered a year ago and expired last week, if I register it again is it going count as registered 1+ year or will it start over?
You will be lucky to get it again. Bet you have to pay a pretty penny. Different registrars charge different amounts. One I have dealt with charges $200 + registration fee. Other registrars may be higher. If you want it back badly enough pay the registrar immediately.
I really don't want the domain back I just wondering if I get it back, will the domain count as 1+ year or will the count start over?
I can't answer your question. If you reregistered it yourself I suspect it would be considered a 1+ year old domain. One of my clients changed her ISP and we failed to notify her registrar of the change, hence she did not get her renewal notices. Her domains expired. She paid the 200 + registration cost and kept her site active. Indexing did not suffer.
One of mine was with namecheap. It had expired and I was unable to renew or reactivate it from the control panel due to the time I'd left, (definately more than 30 days, almost 40 in reality) it appeared like it had left their systems as it wasn't showing. However, I emailed namecheap and they were able to get reactive it for me before it became available to the public. They also put it thought their systems and charged me the regular price of $8.88 good luck