A sequence is defined by means of the recursion Find an explicit formula for
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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
Školjka 
is defined by means of the recursion
