On sequences with {-1,0,1} Hankel transforms

TL;DR

This paper investigates sequences with Hankel transforms in {-1,0,1}, exploring their connection to continued fractions and proposing a conjecture about the distribution of non-zero terms.

Contribution

It introduces a conjecture linking the distribution of non-zero Hankel transform terms to powers in continued fraction expansions.

Findings

Proposes a conjecture relating Hankel transform distribution to continued fractions

Establishes a connection between Hankel transforms and special continued fraction expansions

Provides theoretical insights into the structure of sequences with {-1,0,1} Hankel transforms

Abstract

We study Hankel transforms of sequences, where the transform elements are members of the set {-1,0,1}. We relate these Hankel transforms to special continued fraction expansions. In particular, we posit a conjecture relating the distribution of non-zero terms in the Hankel transform to the distribution of powers of the variable in the defining continued fractions.