Explain the number sequence and predict the next 6 numbers

Given the number sequence

0,1,4,9,0,1,9,1,4,2,1,3,0,4,1,5,4,6,9,7,0,9,9,a,4,?,?,?,?,?,?

the challenge is to

1. Determine the value represented by a
2. Predict the next 6 entries represented by ?

Note that

• rot13(Vf gurer n ernfba jul lbh'ir jevggra "n" naq abg "?") Feb 19 '20 at 10:21
• term "a" was a big give away Feb 19 '20 at 23:02
• Your title says 7 numbers, but everywhere else suggests 6. Feb 20 '20 at 1:48
• @L.F. thanks for the comment.... will fix
– tom
Feb 20 '20 at 10:29
• @DmitryKamenetsky -- Ahh yes. I always find it hard to find a balance between presenting an interesting challenge and making it too easy or too hard. Fair comment.
– tom
Feb 20 '20 at 10:33

The rule of the sequence is:

Write each square number in hexadecimal and reverse it.

0 = 0
1 = 1
4 = 4
9 = 9
16 = 0, 1
25 = 9, 1
36 = 4, 2
49 = 1, 3
64 = 0, 4
81 = 1, 5
100 = 4, 6
121 = 9, 7
144 = 0, 9
169 = 9, a (a represents 10 in hexadecimal)
196 = 4, c
225 = 1, e
256 = 0, 0, 1

• Congratulations :-), nice explanation, well done!
– tom
Feb 20 '20 at 10:34