Generalized Fibonacci Numbers and Blackwell's Renewal Theorem

TL;DR

This paper explores the relationship between generalized Fibonacci numbers and renewal theory, employing Blackwell's renewal theorem to derive approximations and explicit representations with error estimates.

Contribution

It introduces a novel connection between generalized Fibonacci numbers and renewal theory, providing explicit formulas and error bounds.

Findings

Derived an approximation to generalized Fibonacci numbers.

Provided explicit representations with error estimates.

Connected Fibonacci sequences to renewal process theory.

Abstract

We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates in the renewal theorem we figure out an explicit representation.