Automated Generation of Generating Functions Related to Generalized Stern's Diatomic Arrays in the footsteps of Richard Stanley

Abstract

Using Symbolic Dynamic Programming we describe algorithms, fully implemented in Maple, for automatically generating generating functions introduced by Richard Stanley in his study of generalized Stern arrays, generalized even further, to arrays defined in terms of general sequences satisfying linear recurrences with constant coefficients, rather than just the Fibonacci and k-bonacci sequences