The rule of the sequence is:

Write each square number in hexademical and reverse it.

Example & Answer:

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 hexademical)
196 = 4, c
225 = 1, e
256 = 0, 0, 1

The rule of the sequence is:

Write each square number in hexadecimal and reverse it.

Example & Answer:

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