Adjacent Divisibility in the Narayana Triangle

This paper studies divisibility between adjacent entries in the Narayana triangle. An exact divisibility criterion is obtained from the quotient of consecutive Narayana numbers, leading to periodicity and density results for fixed columns. Further results concern the mean number of adjacent divisibilities, unbounded divisibility chains, and connections with related integer sequences. Related OEIS sequence: A400125.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-24
DOI
https://doi.org/10.5281/zenodo.22937686
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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preprint

Adjacent Divisibility in the Narayana Triangle

Felix Huber
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

Adjacent Divisibility in the Narayana Triangle

Felix Huber
preprint en

Abstract

This paper studies divisibility between adjacent entries in the Narayana triangle. An exact divisibility criterion is obtained from the quotient of consecutive Narayana numbers, leading to periodicity and density results for fixed columns. Further results concern the mean number of adjacent divisibilities, unbounded divisibility chains, and connections with related integer sequences. Related OEIS sequence: A400125.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
DOIOpen Access PDFOpenAlex
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Adjacent Divisibility in the Narayana Triangle — Felix Huber · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS