# Recurring Limits

Calculus Level 5

Define a recurrence relation with $$a_{0}=1$$ and $a_{n}=a_{\left\lfloor n/2\right\rfloor}+a_{\left\lfloor n/3 \right\rfloor}+a_{\left\lfloor n/6\right\rfloor}$ If $$\displaystyle\lim_{n\to\infty}\dfrac{a_{n}}{n}=\dfrac{a}{\log{b}}$$ for integers $$a,b,$$, find $$a+b.$$

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