A recurrence relation computes value $d_n$ with the $\{d_{i},d_{j}\ldots\}$ previous digits of the sequenceSo for example, the Fibonacci sequence is defined as follows:$$F_n = F_{n-1}+F_{n-2},\ \ \ F_0=0, F_1=1$$The classic closed form solution is given by the Binet formula:$$F_n = \frac{\phi^n-\psi^n}{\sqrt{5}}$$where $\phi=\frac{1+\sqrt{5}}{2}$ and $\psi=1-\phi$.The question is: are there such sequence of digits defined through some arbitrary recurrence relation that do not have a closed form solution, that is, that provably do not have a closed form solution? I am asking this question in CS stack exchange because the context of this question is Random Number Generation... If such iterated sequences exist, this could be (could be) helpful in designing RNG's... 
Recurrence relations that do not have a closed form solution
recurrence relation;random number generator