Integer Sequences and Output Arrays

TL;DR

This paper introduces a general construction linking various integer sequences, including Catalan-related sequences, providing code and examples to generate new sequences from input data.

Contribution

It presents a novel construction method that unifies and extends known integer sequences, offering tools to generate and analyze new sequences.

Findings

The construction relates Catalan numbers and bracket tournaments sequences.

Some generated sequences are already in OEIS, others are new.

The paper provides code and numerous examples for sequence generation.

Abstract

The first author recently introduced an integer sequence now numbered A355519 in OEIS. This sequence arose from counting bracket tournaments; its study evokes the analysis of the Catalan triangle (sequence A009766 in OEIS) and the related Catalan numbers, sequence A000108 in OEIS. We therefore introduce a general construction that places these sequences on the same footing and suggests many new integer sequences. We provide code for performing this construction and a lengthy list of examples. This construction determines a function from input sequences to output sequences. Some of the resulting output sequences are in OEIS and others are not.