Fibonacci and Lucas Polynomials in n-gon

Abstract

In this paper, we bring into light, study the polygonal structure of Fibonacci polynomials that are placed clockwise on these by a number corresponding to each vertex. Also, we find the relation between the numbers with such vertices. We present a relation for obtained sequence in an n-gon yielding the m-th term formed at k vertices. Also, we apply these situations to Lucas polynomials and find new recurrence relations. Then, the numbers obtained by writing the coefficients of these polynomials in step form are shown in OEIS.

Keywords

• binet formula
• lucas polynomials
• fibonacci polynomials
• recurrence relation
• 11b37
• 11b39