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<p/> <p>We study the asymptotic behavior of the solutions for the following nonlinear difference equation <inline-formula><graphic file="1687-1847-2009-214309-i1.gif"/></inline-formula> where the initial conditions <inline-formula><graphic file="1687-1847-2009-214309-i2.gif"/></inline-formula> are arbitrary nonnegative real numbers, <inline-formula><graphic file="1687-1847-2009-214309-i3.gif"/></inline-formula> are nonnegative integers, <inline-formula><graphic file="1687-1847-2009-214309-i4.gif"/></inline-formula>, and <inline-formula><graphic file="1687-1847-2009-214309-i5.gif"/></inline-formula> are positive constants. Moreover, some numerical simulations to the equation are given to illustrate our results.</p>