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Using the case above, and applying it to recurrence relations, we would write the relation as: $a_n=a_{n-1}+a_{n-2}$ where the initial conditions are $a_0=1$ and $a_1=4$.  \vspace{2mm}  Some of the more well known examples from the study of discrete mathematics include the Fibonacci sequence as well as binomial coefficients. While the Fibonacci sequence defined by $F_n=F_{n-1}+F_{n-2}$ where $F_1=F_2=1$ is fairly easy to recognize as a recurrence relation, binomial coefficients are not primarly primarily  described in this way. However, we see from the following illustration that they can, indeed, be accepted as following a recurrence relation. \[ {n \choose k} = {n-1 \choose k-1} + {n-1 \choose k} \]  \vspace{2mm}