Some identities involving Fibonacci polynomials

Abstract

In this paper we will prove some generalized identities involving k-Fibonacci sequences and Fibonacci polynomials.

On the Quinary Fibonacci-Padovan Sequences

“…Second order linear recurrences related to Fibonacci and Lucas numbers and their generalizations are investigated in [8,14,15,21]. Fourth order linear recurrences and their generalizations are studied in [9,10,20,23]. On algebraic identities on a new integer sequence with four parameters are investigated in [24].…”

“…In [9] and [10] various fourth order linear recurrences and their polynomials are defined and studied.…”

On the Quadra Fibona-Pell and Hexa Fibona-Pell-Jacobsthal Sequences

“…In [3] and [4] various fourth order linear recurrences and their polynomials are defined and studied. In [15] the author define the quadrapell numbers and quadrapell polynomials as fourth order linear recurrences.…”

“…Second order linear recurrences related to Fibonacci and Lucas numbers and their generalizations are investigated in [6], [7], [11], [14]. Fourth order linear recurrences and their generalizations are studied in [3], [4], [13], [15].…”

“…In [3] and [4] various fourth order linear recurrences and their polynomials are defined and studied.…”