Pattern Avoidance for Fibonacci Sequences using $k$-Regular Words

Emily Downing, Elizabeth Hartung, Cody Lucido +1

Two $k$-ary Fibonacci recurrences are $a_k(n)=a_k(n-1)+k\cdot a_k(n-2)$ and $b_k(n)=k\cdot b_k(n-1)+b_k(n-2)$. We provide a simple proof that $a_k(n)$ is the number of $k…