A Note on the Control of Mortality for Nested Recurrence Relation $H(n)=H(n-H(n-2))+H(n-H(n-3))$

TL;DR

This paper explores the properties and control mechanisms of a specific nested recurrence relation, expanding understanding of its behavior through recent analytical approaches.

Contribution

It introduces new insights into the control of the $H$-recurrence defined by $H(n)=H(n-H(n-2))+H(n-H(n-3))$ using recent methods for analyzing complex recurrences.

Findings

Characterization of the $H$-recurrence behavior

Identification of conditions for recurrence stability

Application of recent analytical approaches to nested recurrences

Abstract

In this work, we investigate $H$-recurrence which is defined by $H(n) = H(n-H(n-2)) + H(n-H(n-3))$ thanks to a recent approach to certain recurrences such as Conway and Hofstadter $Q$ recursions.