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$(\forall n \in \mathbb{Z})\left[ {{a_{n + 2}} = {a_n}{a_{n + 1}} + {b_n}{c_{n + 1}} + {b_{n + 1}}{c_n} \wedge {b_{n + 2}} = {a_n}{b_{n + 1}} + {b_n}{a_{n + 1}} + {c_n}{c_{n + 1}} \wedge {c_{n + 2}} = {a_n}{c_{n + 1}} + {b_n}{b_{n + 1}} + {a_{n + 1}}{c_n}} \right]$，若$a_{1}=a_{2}=1，b_{1}=c_{4}=0，b_{2}=2，c_{2}=3$,求$\{a_n\},\{b_n\},\{c_n\}$ |
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