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This is an example of a recurrence relation. We represented one instance of our counting problem in terms of two simpler instances of the problem. If only we knew the cardinalities of \(\B^4_2\) and \(\B^4_3\text{.}\) Repeating the same reasoning,

\begin{equation*} |\B^4_2| = |\B^3_1| + |\B^3_2| \quad \mbox{and} \quad |\B^4_3| = |\B^3_2| + |\B^3_3|\text{.} \end{equation*}

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