Note on sequences A123192, A137396 and A300453

2019/11/11 by Franck Ramaharo, Ramaharo, Franck
Computer Science · Engineering · Mathematics · #05A10 #57M25 #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.CO #math.GT #msc:05A10 #msc:57M25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1911.04528

LateX, 6 pages, 3 figures, 3 tables, 3 OEIS A-numbers

arxiv created 2019/11/11 · openalex publication_date 2019/11/11 · arxiv updated 2019/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give the connection between three polynomials that generate triangles in The On-Line Encyclopedia of Integer Sequences (A123192, A137396 and A300453). We show that they are related with the bracket polynomial for the (2,n)-torus knot

Citations

• A state enumeration of the foil knot

Related

• An Unknotting Sequence for Torus Knots
• An explicit formula for the A-polynomial of the knot with Conway's notation C(2n, 3)
• An explicit formula for the A-polynomial of the knot with Conway's notation C(2n, 4)
• A recursive relation in the (2p+1,2) torus knot
• Patterns of the V₂-polynomial of knots