Solving a difference equation with two variables

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Consider the following difference equation: $$ {c_1}{a_{n + 3}} + {c_2}{a_{n + 2}} + {c_3}{b_{n + 2}} + {c_4}{p_{n + 2}} + {c_5}{p_{n + 1}} + {c_6}{p_{n + 3}} + {c_7}{p_{n + 3/2}} + {c_8}{p_{n + 5/2}} = 0 $$ where the unknowns are: $$ {a_{n}},{b_{n}} $$ and are to be determined in terms of $${p_{n}},{p_{n+1}},...$$ Is there any way to obtain the unknowns by transforming the difference equation into an algebraic one? or transfer the unknowns from points n+3, n+2, ... to n?