IMO Shortlist 1981 problem 9


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2. travnja 2012.
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A sequence (a_n) is defined by means of the recursion
a_1 = 1, a_{n+1} = \frac{1 + 4a_n +\sqrt{1+ 24a_n}}{16}.
Find an explicit formula for a_n.
Izvor: Međunarodna matematička olimpijada, shortlist 1981