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

TL;DR

This paper presents algorithms implemented in Maple for automatically generating functions related to generalized Stern arrays, extending Stanley's work to arrays based on linear recurrence sequences beyond Fibonacci and k-bonacci.

Contribution

It introduces a symbolic dynamic programming approach to derive generating functions for a broad class of arrays defined by linear recurrences, expanding previous combinatorial frameworks.

Findings

Algorithms successfully generate functions for generalized arrays

Implementation in Maple demonstrates practical applicability

Extends Stanley's methods to new sequence classes

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