A $q$-analogue of the Biperiodic Fibonacci Sequence

José L. Ramírez, Víctor Sirvent

The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation $t_n=a{t}_{n-1}+t_{n-2}$ if $n$ is even, $t_n=b{t}_{n-1}+t_{n-2}$ if $n$ is odd, with i…