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In this paper, we find the asymptotic behavior of solutions of the third order difference equationxn+1=xn-21+pxn+qxn-1+xn-2,n=0,1,2,…for all admissible non-negative values of the parameters p,q where the initial conditions x −2 ,x −1 ,x 0 are positive. We show that the solutions do not exhibit a periodic attitude for all parameters of the above mentioned difference equation...
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