Palindromic length sequence of the ruler sequence and of the period-doubling sequence

TL;DR

This paper investigates the palindromic length sequences of the ruler and period-doubling sequences, providing explicit formulas and bounds to deepen understanding of their combinatorial properties.

Contribution

It offers a precise formula for the palindromic length sequence of the ruler sequence and establishes a lower bound for the period-doubling sequence's sequence, advancing combinatorial sequence analysis.

Findings

Explicit formula for the ruler sequence's palindromic length sequence

Lower bound for the limit superior of the period-doubling sequence's palindromic length

Enhanced understanding of palindromic structures in these sequences

Abstract

In this article, we study the palindromic length sequences of the ruler sequence and of the period-doubling sequence. We give a precise formula of the palindromic length sequence of the first one and find a lower bound of the limit superior of the palindromic length sequence of the last one.