A Modular Recursion Sequence?

Let recursion aia_i be defined as:

an=an1+an2(mod10)a_n=a_{n-1}+a_{n-2} \pmod{10}

where all terms in the sequence are positive integers less than ten. For any given a1a_1 and a2a_2, a distinct sequence is formed. For example, if a1=5a_1=5 and a2=4a_2=4, the sequence would go 5, 4, 9, 3, 2, 5, 7, 2, 9, 1, so on and so forth. If a6=6a_6=6, find the sum of all possible values of a1a_1.

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