Note on sequences A123192, A137396 and A300453

TL;DR

This paper explores the relationship between three integer sequence-generated polynomials and their connection to the bracket polynomial of the (2,n)-torus knot, revealing new links between combinatorics and knot theory.

Contribution

It establishes a novel connection between specific integer sequence polynomials and the bracket polynomial of a class of knots, enriching the understanding of their mathematical interplay.

Findings

Identifies the connection between three sequence-generating polynomials and knot invariants.

Shows these polynomials are related to the bracket polynomial for (2,n)-torus knots.

Provides new insights into the interplay between combinatorics and knot theory.

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