Multivariable Lucas Polynomials and Lucanomials

Edward E. Allen, Katherine Riley, Michael Weselcouch

Lucas polynomials are polynomials in $s_1$ and $s_2$ defined recursively by $\{0\}=0$, $\{1\}=1$, and $\{m\}=s_1\{m-1\}+s_2\{m-2\}$ for $m\ge 2$. We generalize Lucas polynomials…