Parents Eligible to use AOC Credit ?

[RWG1950]

I'm having trouble getting my head around an AOC calculation when a 529 distribution is involved.
Taxpayers have a 22 year old dependent daughter in her 4th year at a university.
She has used 3 prior years of AOC & seems to meet the other qualifications for 2018.
Her 2018 1098-T shows $ 7,746 in tuition. (Verified as paid) No scholarships or other ed. assistance.
A 2018 distribution of $ 7,771 was taken from her 529 plan. The 1099-Q shows $ 2,574 earnings $ 5,196 basis
Using $ 7,746 tuition minus the $ 4,000 for the AOC, I get $3,746 of AQEE.
Following the example on page 53 of IRS pub 970 it would seem that $ 1,334 of her 529 distribution is taxable to her.
As I understand it, the daughter is to claim the $ 1,334 on her return & the parents use her full AOC on theirs.
Do I have this figured right ?
Thanks for comments.

[ATSMAN]

529 distribution can be used to pay for room and board, books and supplies, computer and internet, special equipment etc. So the way I do the calculation is leave 4000 for AOC and have the rest paid with 529 proceeds.

[TaxGuyBill]

My math got $1,333 (rather than your $1,334), but close enough.

However, what about Room & Board? Even if the student lives with the parent, 529 plans can still be applied towards some Room & Board (have them ask the college financial aid office for the amount of the housing allowance for students living with their parents).