|Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6|
Robinson A. Higuita
Instituto de Matemáticas
Universidad de Antioquia Medellín
Department of Mathematics and Computer Science
Charleston, SC 29409
We generalize the numerical recurrence relation given by Hosoya to polynomials by constructing a Hosoya triangle for polynomials where each entry is either a product of two polynomials of Fibonacci-type or a product of two polynomials of Lucas-type. For every such choice of polynomial sequence we obtain a triangular array of polynomials. In this paper we extend the star of David property, also called the Hoggatt-Hansell identity, to these types of triangles. In addition, we study other geometric patterns in these triangles and as a consequence we obtain geometric interpretations for the Cassini identity, the Catalan identity, and other identities for Fibonacci polynomials.
(Concerned with sequences
Received May 31 2017; revised versions received March 5 2018; March 20 2018; April 15 2018. Published in Journal of Integer Sequences, May 8 2018.