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<p/> <p>The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation <inline-formula><graphic file="1687-1847-2010-970720-i1.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-970720-i2.gif"/></inline-formula>, where the parameters <inline-formula><graphic file="1687-1847-2010-970720-i3.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-970720-i4.gif"/></inline-formula> is an integer, and the initial conditions <inline-formula><graphic file="1687-1847-2010-970720-i5.gif"/></inline-formula>. It is shown that the unique positive equilibrium of the equation is globally asymptotically stable under the condition <inline-formula><graphic file="1687-1847-2010-970720-i6.gif"/></inline-formula>. The result partially solves the open problem proposed by Kulenovi&#263; and Ladas in work (2002).</p>