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We give an asymptotic Binet-type formula for such sequences. We compare $(a_n)$ with a natural linear recurrence sequence (lrs) $(\\tilde{a}_n)$ associated with it and prove under certain assumptions that the difference sequence $(a_n- \\tilde{a}_n)$ tends to infinity. 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We give an asymptotic Binet-type formula for such sequences. We compare $(a_n)$ with a natural linear recurrence sequence (lrs) $(\\tilde{a}_n)$ associated with it and prove under certain assumptions that the difference sequence $(a_n- \\tilde{a}_n)$ tends to infinity. 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