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 \(a+b.\)

This is part of Ordered Disorder.
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